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Lauterbach, Dominic [Verfasser]. "Singular Mixture Copulas - A Geometric Method of Constructing Copulas / Dominic Lauterbach." München : Verlag Dr. Hut, 2014. http://d-nb.info/1052375359/34.
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Blom, Joakim, and Joakim Wargclou. "Does copula beat linearity? : Comparison of copulas and linear correlation in portfolio optimization." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-124634.
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Modern portfolio theory (MPT) is an investment theory which was introduced by Harry Markowitz in 1952 and describes how risk averse investors can optimize their portfolios. The objective of MPT is to assemble a portfolio by maximizing the expected return given a level of market risk or minimizing the market risk given an expected return. Although MPT has gained popularity over the years it has also been criticized for several theoretical and empirical shortcomings such as using variance as a measure of risk, measuring the dependence with linear correlation and assuming that returns are normally distributed when in fact empirical data suggests otherwise. When moving away from the assumption that returns are elliptical distributed, for example normally distributed, we can not use linear correlation as a measure of dependence in an accurate way. Copulas are a flexible tool for modeling dependence of random variables and enable us to separate the marginals from any joint distribution in order to extract the dependence structure. The objective of this paper was to examine the applicability of a copula-CVaR framework in portfolio optimization compared to the traditional MPT. Further, we studied how the presence of memory, when calibrating the copulas, affects portfolio optimization. The marginals for the copula based portfolios were constructed using Extreme Value Theory and the market risk was measured by Conditional Value at Risk. We implemented a dynamic investing strategy where the portfolios were optimized on a monthly basis with two different length of rolling calibration windows. The portfolios were backtested during a sample period from 2000-2016 and compared against two benchmarks; Markowitz portfolio based on normally distributed returns and an equally weighted, non optimized portfolio. The results demonstrated that portfolio optimization is often preferred compared to choosing an equally weighted portfolio. However, the results also indicated that the copula based portfolios do not always beat the traditional Markowitz portfolio. Furthermore, the results indicated that the choice of length of calibration window affects the selected portfolios and consequently also the performance. This result was supported both by the performance metrics and the stability of the estimated copula parameters.
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Schmitz, Volker. "Copulas and stochastic processes." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=972691669.
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Zeng, Xuexing. "Copulas for image processing." Thesis, University of Strathclyde, 2010. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=14336.
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Mazzoli, Maria. "Copulas in Nigerian Pidgin." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3422599.
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In this work I describe the copular system of Nigerian Pidgin (NigP), a pidgin/creole language spoken in Nigeria. I restricted the analysis to the modern Western metropolitan variety. I built the present work upon both corpus occurrences and grammaticality judgments and, as I explain in Chapter 2, the spoken corpus of NigP was collected during field research in Lagos in 2007; later, I added to this material a sample of written NigP texts. This combined corpus counts about 100.000 words and is accessible in the CD (Appendix A-CD and B-CD). In 2012 I conducted a prosodic experiment in collaboration with the Paduan CNR on the tonal realisation of DE in the spoken production of two speakers from Benin City. This elicited material is also available in Appendix C-CD. I divided the space covered by copulas in NigP into three semantic domains: (1) identification/ascription, (2) location/existence, and (3) attribution. The choice of the copula in NigP is mainly grounded on the syntactic nature of the complement. Thus, the copulas be and na govern nominal complements in identificational and ascriptive contexts, the copula de governs locative arguments or displays intransitively in existential contexts, and the attributive copula de is inserted in the verb slot before verbal property item if certain conditions are met. I deal with these issues in the three research chapters (4, 5 and 6 respectively). The main aim was to attest and explain the variation encountered in each domain. In Chapter 4 I explain that the focus introducer na has been reanalysed as a copula in identificational and ascriptive contexts. In fact, the copular constructions with be and na entail two different pragmatic and syntactic encodings of their arguments, which explains the perfect complementary distribution of the two items. In Chapter 5 I deal with the lexical item DE, which encompasses two grammatical categories: existential/locative copula and imperfective aspect. Speakers realise the difference between the two by means of tone, as the results of the prosodic experiment consistently confirmed. Attributive contexts are not always copular due to the verbal nature of property items, as I claim in Chapter 6. The insertion of the copula de is governed by diverse syntactic and semantic factors. Also, the prosodic experiment conducted on the tonal realisation of DE allowed attesting the fluctuating aspectual character (stative/non-stative) of property items in NigP and, consequently, their occurrence with both the high-toned copula de and the low-toned imperfective marker dè.Questo lavoro descrive il sistema delle copule in Nigerian Pidgin (NigP), una lingua pidgin/creola parlata in Nigeria. Ho ristretto l’analisi alla varietà odierna parlata in contesti metropolitani nell’Ovest del paese. Le fonti dei dati sono le occorrenze del corpus e i giudizi di grammaticalità forniti dagli informatori. Come spiego nel Capitolo 2, il corpus parlato di NigP è stato registrato durante una ricerca sul campo nella città di Lagos mentre in seguito ho aggiunto a questi dati alcuni esempi di produzioni scritte di NigP. L’intero corpus è consultabile sul CD allegato (Appendici A-CD e B-CD). Nel 2012 ho condotto un esperimento prosodico in collaborazione con il CNR di Padova sulla realizzazione tonale dell’elemento DE sulla base della produzione orale di due parlanti originarie di Benin City. Anche questo materiale elicitato è disponibile su CD (Appendice C-CD). Ho diviso lo spazio semantico coperto dalle copule in NigP in tre macro-aree: (1) identificazione/ascrizione, (2) locazione/esistenza, e (3) attribuzione. La scelta della copula in NigP è basata sulla natura sintattica del complemento. Infatti, le copula be e na reggono complementi nominali nei contesti identificazionali e ascrittivi, la copula de regge complementi locativi o si trova come esistenziale intransitivo, e la copula attributiva de può essere inserita prima dei lessemi (verbali) che esprimono la proprietà se si danno alcune condizioni. Affronto questi temi nei tre capitoli di ricerca (rispettivamente il 4, 5 e 6). Lo scopo principale era di descrivere e spiegare la variazione che si trova in ciascuna macro-area semantica. Nel Capitolo 4 spiego come l’introduttore di focus na sia stato rianalizzato come copula in contesti identificazionali e ascrittivi. Infatti le copule be e na comportano due diverse codifiche sintattiche e pragmatiche dei loro argomenti e questo spiega la perfetta distribuzione complementare dei due elementi. Nel Capitolo 5 descrivo l’elemento lessicale DE, che comprende due categorie grammaticali: copula esistenziale/locativa e aspettuale imperfettivo. La differenza tra le due è realizzata dai parlanti grazie ad una distinzione tonale, come hanno dimostrato i risultati dell’esperimento prosodico. I contesti attributivi non sono sempre copulari perché i lessemi che esprimono proprietà in NgP sono verbali, come sostengo nel Capitolo 6. L’inserzione della copula de è governata da diversi fattori sintattici e pragmatici. Inoltre, l’esperimento prosodico sulla realizzazione tonale di DE ha permesso di attestare l’oscillazione aspettuale di questi elementi verbali esprimenti una proprietà (stativo/non-stativo) e, di conseguenza, la loro occorrenza sia con la copula de (tono alto) che con il marcatore preverbale imperfettivo dè (tono basso).
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Harder, Michael [Verfasser]. "Exchangeability of copulas / Michael Harder." Ulm : Universität Ulm, 2016. http://d-nb.info/1106329910/34.
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Kakouris, Iakovos. "Applications of copulas in optimisation." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/33163.
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The methods for modelling uncertainty and assessing the risk of financial markets were placed under scrutiny after the 2008 crisis. To protect against the worst possible scenario, in a problem of asset allocation, robust optimisation is required. Still, within this framework, assumptions about the uncertainty set have to be made. In our work, we expand the possible options for describing uncertainty sets, through the use of copulas. Copulas are a useful tool for describing uncertainty because of the modelling flexibility that they provide. They are able to easily describe asymmetric dependence structures and tail risk. Both are vital for emulating the financial markets behaviour, during periods of extreme shocks and comovements. Also, copulas are associated with robust measures of dependence. We introduce copulas into the robust optimisation framework by following two different approaches. At first, we derive a Worst Case Conditional Value at Risk optimisation problem, in which the uncertainty set consists of a selection of copulas. We formulate the problem into a convex optimisation problem. The advantages of such a model are supported by numerical examples using real data. In the second approach, copulas are used as means for creating non-symmetric, convex uncertainty sets, in the form of domains. We present examples where these sets can be used in a robust optimisation problem.
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Viola, Márcio Luis Lanfredi 1978. "Teoria de valores extremos e copulas : distribuição valor extremo generalizada e copulas arquimedianas generalizadas trivariadas." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306675.
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Orientadores: Veronica Andrea Gonzales-Lopez, Laura Leticia Ramos RifoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-07T14:24:13Z (GMT). No. of bitstreams: 1 Viola_MarcioLuisLanfredi_M.pdf: 24648946 bytes, checksum: 3e9e740e3961441870b59a758583d5af (MD5) Previous issue date: 2006
Resumo: Sob a ótica da Teoria de Cópulas, a modelagem multidimensional pode ser considerada decorrente de dois processos: estimação das funções de distribuição acumulada marginais e modelagem de uma estrutura de dependência multidimensional que age sobre tais funções de distribuição marginais, sendo esta última, denominada cópula. Neste trabalho, as funções de distribuição acumulada marginais de interesse correspondem à função de distribuição acumulada do máximo de uma variável aleatória e, consequentemente, a Teoria de Valores Extremos apresenta-se como uma alternativa natural para a modelagem das distribuições marginais. Nesta dissertação, serão estudados os tipos de dependência entre variáveis aleatórias, a construção e implementação de modelos de Teoria de Cópulas assim como, os resultados básicos de convergência utilizados na Teoria de Valores Extremos. Sob o escopo da Teoria de Valores Extremos, os métodos de estimação pontual de Máxima Verossimilhança e L-momentos serão comparados através de algumas simulações e, adicionalmente, serão abordadas as condições que asseguram a validade das propriedades assintóticas do Método de Máxima Verossimilhança bem como as principais propriedades de ambos os métodos citados. As teorias citadas serão aplicadas no contexto de Lingüística na modelagem multidimensional de características do sinal acústico observadas em regiões de baixa, média e alta freqüência de frases das línguas inglesa e francesa
Abstract: In the copula theory we can interpret a multidimensional distribution as a result of two processes, namely, marginal cumulative distribution function estimation and dependence structure estimation. The latter, called copula, is employed to aggregate the marginal distributions. In this work, the marginal distributions correspond to the maximum value of random variables. Thus, the extreme value theory, in particular the generalized extreme value distribution, is a natural way to model the marginal distribution. Some theoretical aspects will be studied in order to obtain knowledge the principal results of concerning the convergence in distribution associated with maximum likelihood estimation and L-moments estimation. This strategy is essential because the generalized extreme value distribution represents a nonregular case. Some simulation were performed in order to compare the behavior of the method. We will also take into account trivariate copula models such as Kimeldorf and Sampson model and Gumbel model. We will use maximum likelihood method for the point estimation in copula models. Finally, we will apply extreme value theory and copula model in a linguistic problem. Preciselly, we will consider signal coming from the three different frequence classes modeled both English and French languages
Mestrado
Mestre em Estatística
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Krupskii, Pavel. "Structured factor copulas and tail inference." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/48390.
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In this dissertation we propose factor copula models where dependence is modeled via one or several common factors. These are general conditional independence models for $d$ observed variables, in terms of $p$ latent variables and the classical multivariate normal model with a correlation matrix having a factor structure is a special case. We also propose and investigate dependence properties of the extended models that we call structured factor copula models. The extended models are suitable for modeling large data sets when variables can be split into non-overlapping groups such that there is homogeneous dependence within each group. The models allow for different types of dependence structure including tail dependence and asymmetry. With appropriate numerical methods, efficient estimation of dependence parameters is possible for data sets with over 100 variables.
The choice of copula is essential in the models to get correct inferences in the tails. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in factor copula models as well as for assessing the adequacy of fit of multivariate copula models.
We apply the structured factor copula models to analyze financial data sets, and compare with other copula models for tail inference. Using model-based interval estimates, we find that some commonly used risk measures may not be well discriminated by copula models, but tail-weighted dependence measures can discriminate copula models with different dependence and tail properties.Science, Faculty of
Statistics, Department of
Graduate
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Schmitz, Volker [Verfasser]. "Copulas and Stochastic Processes / Volker Schmitz." Aachen : Shaker, 2003. http://d-nb.info/1179023064/34.
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Duarte, Cláudia Catarina Acúrcio. "Copulas and defaults within a crisis." Master's thesis, Instituto Superior de Economia e Gestão, 2010. http://hdl.handle.net/10400.5/2252.
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Mestrado em Matemática FinanceiraIn the aftermath of the subprime crisis, the main purpose of this thesis is to as-sess the default dependency among firms, studying the case of four US financial institutions in two periods of time: before and during the crisis. The methodology followed is based on conditional copula models, which provides a set of global and tail dependency measures, beyond the linear correlation widely misused in financial problems. For this purpose, we use CDS (credit default swap) data to estimate the copulas, that are assumed to be a proxy for default closeness, as they reflect the credit risk of the institutions. As far as we know, this is a novelty of the present analysis. The usual practice is to use equity returns, which are incomplete and more indirect indicators of defaults. The procedures are carried out in two steps. First, we model the individual dynamics for defaults closeness, by using ARMA-GARCH specifications applied to CDS spreads variations and assuming t-distributed innova¬tions (to capture the extreme observations). Then, we fit a set of copula functions to the standardised residuals of the marginal distributions. The best specifications for the characterisation of the dependency structure are different for the two sub-periods analysed, confirming a structural break in the default dependency pattern, occurred in the summer of 2007. The results also confirm our expectations regarding the global dependency under stressful scenarios. For the four considered financial institutions, all the dependency measures rose substantially in the crisis period. Furthermore, we observe a significant increase in the upper tail dependency, corre¬sponding to high probabilities of simultaneous defaults. These outcomes point out to the increase of the systemic and contagion risks in the US financial markets.
No rescaldo da crise do subprime, o principal objectivo desta tese e avaliar a de¬pendência entre os defaults de empresas, estudando o caso de quatro instituicoes financeiras americanas em dois períodos: antes e durante a crise. A metodologia utilizada baseia-se em modelos de copulas condicionadas, que fornecem um conjunto de medidas de dependencia global e de cauda, complementando a correlacao linear indevidamente utilizada nos problemas financeiros. Para esse efeito, usamos os CDS para estimar cópulas, que sao assumidos como proxy para a proximidade ao default, dado que reflectem o risco de credito das instituicoes. Tanto quanto sabemos, esta óe uma novidade da presente anaólise. A praótica usual óe utilizar rendibilidades das accões, que sao um indicador incompleto e mais indirecto dos defaults. Os procedi-mentos sao realizados em duas etapas. Primeiro, sao modelizadas as dinamicas indi¬viduais para a proximidade aos defaults, usando especificares ARMA-GARCH para as variacões dos CDS spreads e assumindo que as inovacoes seguem a distribuyo t-student (para captar as observacoes extremas). De seguida, ajustamos um con¬junto de funcoes copula para os residuos standardizados das distribuições marginais. As melhores especificacões para a caracterizacao da estrutura de dependencia sao diferentes para os dois sub-periodos analisados, confirmando uma quebra estrutural no padrao de dependencia dos defaults, ocorrida no Verao de 2007. Os resulta¬dos tambem confirmam as nossas expectativas relativamente a dependencia global em cenarios de stress. Para os quatro bancos considerados, todas as medidas de dependencia aumentaram substancialmente no periodo de crise. Alem disso, obser¬vamos um aumento significativo da dependencia na cauda direita, o que corresponde a uma elevada probabilidade de defaults simultâneos. Estes resultados apontam para o aumento do risco sistemico e de contógio nos mercados financeiros dos EUA.
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Cuberos, Andres. "Modélisation de la dépendance et estimation du risque agrégé." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10321/document.
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Cette thèse porte sur l'étude de la modélisation et estimation de la dépendance des portefeuilles de risques et l'estimation du risque agrégé. Dans le Chapitre 2, nous proposons une nouvelle méthode pour estimer les quantiles de haut niveau pour une somme de risques. Elle est basée sur l'estimation du rapport entre la VaR de la somme et la VaR du maximum des risques. Nous utilisons des résultats sur les fonctions à variation régulière. Nous comparons l'efficacité de notre méthode avec quelques estimations basées sur la théorie des valeurs extrêmes, sur plusieurs modèles. Notre méthode donne de bons résultats lors de l'approximation de la VaR à des niveaux élevés lorsque les risques sont fortement dépendants et au moins l'un des risques est à queue épaisse. Dans le Chapitre 3, nous proposons une procédure d'estimation pour la distribution d'un risque agrégé basée sur la copule échiquier. Elle permet d'obtenir de bonnes estimations à partir d'un petit échantillon de la loi multivariée et une connaissance complète des lois marginales. Cette situation est réaliste pour de nombreuses applications. Les estimations peuvent être améliorées en incluant dans la copule échiquier des informations supplémentaires (sur la loi d'un sous-vecteur ou sur des probabilités extrêmes). Notre approche est illustrée par des exemples numériques. Finalement, dans le Chapitre 4, nous proposons un estimateur de la mesure spectrale basé sur l'estimation à noyau de la densité de la mesure spectrale d'une distribution à variation régulière bivariée. Une extension de notre méthode permet d'estimer la mesure spectrale discrète. Certaines propriétés de convergence sont obtenuesThis thesis comprises three essays on estimation methods for the dependence between risks and its aggregation. In the first essay we propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We use results on regularly varying functions. We compare the efficiency of our method with classical ones, on several models. Our method gives good results when approximating the VaR or TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed. In the second essay we propose an estimation procedure for the distribution of an aggregated risk based on the checkerboard copula. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard copula some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples. In the third essay we propose a kernel based estimator for the spectral measure density of a bivariate distribution with regular variation. An extension of our method allows to estimate discrete spectral measures. Some convergence properties are obtained
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Dushimimana, Jean Claude. "Pricing multi-asset options with levy copulas." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6699.
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Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011.Imported from http://etd.sun.ac.za
ENGLISH ABSTRACT: In this thesis, we propose to use Levy processes to model the dynamics of asset prices. In the first part, we deal with single asset options and model the log stock prices with a Levy process. We employ pure jump Levy processes of infinite activity, in particular variance gamma and CGMY processes. We fit the log-returns of six stocks to variance gamma and CGMY distributions and check the goodness of fit using statistical tests. It is observed that the variance gamma and the CGMY distributions fit the financial market data much better than the normal distribution. Calibration shows that at given maturity time the two models fit into the option prices very well. In the second part, we investigate the effect of dependence structure to multivariate option pricing. We use the new concept of Levy copula introduced in the literature by Tankov [40]. Levy copulas allow us to separate the dependence structure from the behavior of the marginal components. We consider bivariate variance gamma and bivariate CGMY models. To model the dependence structure between underlying assets we use the Clayton Levy copula. The empirical results on six stocks indicate a strong dependence between two different stock prices. Subsequently, we compute bivariate option prices taking into account the dependence structure. It is observed that option prices are highly sensitive to the dependence structure between underlying assets, and neglecting tail dependence will lead to errors in option pricing.
AFRIKAANSE OPSOMMING: In hierdie proefskrif word Levy prosesse voorgestel om die bewegings van batepryse te modelleer. Levy prosesse besit die vermoe om die risiko van spronge in ag te neem, asook om die implisiete volatiliteite, wat in finansiele opsie pryse voorkom, te reproduseer. Ons gebruik suiwer–sprong Levy prosesse met oneindige aktiwiteit, in besonder die gamma– variansie (Eng. variance gamma) en CGMY–prosesse. Ons pas die log–opbrengste van ses aandele op die gamma–variansie en CGMY distribusies, en kontroleer die resultate met behulp van statistiese pasgehaltetoetse. Die resultate bevestig dat die gamma–variansie en CGMY modelle die finansiele data beter pas as die normaalverdeling. Kalibrasie toon ook aan dat vir ’n gegewe verstryktyd die twee modelle ook die opsiepryse goed pas. Ons ondersoek daarna die gebruik van Levy prosesse vir opsies op meervoudige bates. Ons gebruik die nuwe konsep van Levy copulas, wat deur Tankov[40] ingelei is. Levy copulas laat toe om die onderlinge afhanklikheid tussen bateprysspronge te skei van die randkomponente. Ons bespreek daarna die simulasie van meerveranderlike Levy prosesse met behulp van Levy copulas. Daarna bepaal ons die pryse van opsies op meervoudige bates in multi–dimensionele exponensiele Levy modelle met behulp van Monte Carlo–metodes. Ons beskou die tweeveranderlike gamma-variansie en – CGMY modelle en modelleer die afhanklikheidsstruktuur tussen onderleggende bates met ’n Levy Clayton copula. Daarna bereken ons tweeveranderlike opsiepryse. Kalibrasie toon aan dat hierdie opsiepryse baie sensitief is vir die afhanlikheidsstruktuur, en dat prysbepaling foutief is as die afhanklikheid tussen die sterte van die onderleggende verdelings verontagsaam word.
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Fuchs, Sebastian. "Transformations of Copulas and Measures of Concordance." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-196039.
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Copulas are real functions representing the dependence structure of the distribution of a random vector, and measures of concordance associate with every copula a numerical value in order to allow for the comparison of different degrees of dependence.
We first introduce and study a group of transformations mapping the collection of all copulas of fixed but arbitrary dimension into itself. These transformations may be used to construct new copulas from a given one or to prove that certain real functions on the unit cube are indeed copulas. It turns out that certain transformations of a symmetric copula may be asymmetric, and vice versa.
Applying this group, we then propose a concise definition of a measure of concordance for copulas. This definition, in which the properties of a measure of concordance are defined in terms of two particular subgroups of the group, provides an easy access to the investigation of invariance properties of a measure of concordance. In particular, it turns out that for copulas which are invariant under a certain subgroup the value of every measure of concordance is equal to zero.
We also show that the collections of all transformations which preserve symmetry or the concordance order or the value of every measure of concordance each form a subgroup and that these three subgroups are identical.
Finally, we discuss a class of measures of concordance in which every element is defined as the expectation with respect to the probability measure induced by a fixed copula having an invariance property with respect to two subgroups of the group. This class is rich and includes the well-known examples Spearman's rho and Gini's gamma.
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Muhammad, Noryanti. "Predictive inference with copulas for bivariate data." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11597/.
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Nonparametric predictive inference (NPI) is a statistical approach with strong frequentist properties, with inferences explicitly in terms of one or more future observations. NPI is based on relatively few modelling assumptions, enabled by the use of lower and upper probabilities to quantify uncertainty. While NPI has been developed for a range of data types, and for a variety of applications, thus far it has not been developed for multivariate data. This thesis presents the rst study in this direction. Restricting attention to bivariate data, a novel approach is presented which combines NPI for the marginals with copulas for representing the dependence between the two variables. It turns out that, by using a discretization of the copula, this combined method leads to relatively easy computations. The new method is introduced with use of an assumed parametric copula. The main idea is that NPI on the marginals provides a level of robustness which, for small to medium-sized data sets, allows some level of misspecication of the copula. As parametric copulas have restrictions with regard to the kind of dependency they can model, we also consider the use of nonparametric copulas in combination with NPI for the marginals. As an example application of our new method, we consider accuracy of diagnostic tests with bivariate outcomes, where the weighted combination of both variables can lead to better diagnostic results than the use of either of the variables alone. The results of simulation studies are presented to provide initial insights into the performance of the new methods presented in this thesis, and examples using data from the literature are used to illustrate applications of the methods. As this is the rst research into developing NPI-based methods for multivariate data, there are many related research opportunities and challenges, which we briefly discuss.
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Kpanzou, Tchilabalo Abozou. "Aspects of copulas and goodness-of-fit." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019/1949.
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Riccetti, Luca. "Use of copulas and active portfolio management." Doctoral thesis, Università Politecnica delle Marche, 2010. http://hdl.handle.net/11566/242206.
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Ghassani, Mohamad. "Dynamiques épidémiques, risques et copules." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENS027/document.
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Les modèles stochastiques classiques comportent des copules d'interactions linéaires, exprimant en général des interactions de paire. Il sera envisagé d'étendre ces modèles à des interactions non linéaires de type saturation ou de type triplet, en vue de traiter des applications réalistes, comme les diffusions épidémiques.Le but de cette thèse est d'introduire les fonctions copules en épidémiologie, et surtout d'appliquer ces fonctions sur le système de transmission de la Malaria afin de constater la dépendance entre les différents compartiments du système. Nous étudierons quelques modèles compartimentaux, qui sont une généralisation du modèle de Ross-Macdonald, en supposant que la population n'est pas constante et en prenant en compte des paramètres de transmission comme la fécondité, la mortalité et autres. Aussi, nous introduirons les classes d'âges dans certains de ces modèles compartimentaux, afin de trouver une relation entre les individus de ces classes d'âges à l'aide du modèle de Cox et des fonctions copules. Nous donnerons ensuite, deux exemples sur ces modèles : la Malaria au Mali et la peste en Europe au moyen-âge. Nous introduirons aussi les quantiles conditionnels et les fonctions copules archimédiennes, ce qui nous mènera à trouver une dépendance entre les différents compartiments des hôtes et des vecteursThe stochastic classical models include linear interactions copulas, expressing in general pair interactions. It is planned to extend these models to nonlinear interactions of saturation type or triplet type, to treat realistic applications, as the epidemics diffusions.The aim of this thesis is to apply the copulas functions in epidemiology, and especially to apply these functions in the transmission system of malaria to detect the dependence existing between compartments of the epidemic system. We will study some compartmental models, which are a generalization of the Ross-Macdonald model, assuming that the population is not constant and taking into account the transmission parameters such as fertility, mortality, etc. Also, we will introduce the age classes in some of these compartmental models, and study the relationships between individuals of these age classes, using the Cox model and the copulas functions. Then, we will give two examples of these models: the Malaria in Mali and the plague in Europe during the Middle Ages. We will introduce also the conditional quantiles and the Archimedean copulas functions, that will lead us to find dependencies between the different compartments of hosts and vectors
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Nystedt, Gustav. "Scenario Creation for Stress Testing Using Copula Transformation." Thesis, Umeå universitet, Institutionen för fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-160352.
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Due to turbulence in the financial market throughout history, stress testing has become a growing part of the risk analysis performed by clearing houses. Events connected to previous crises have increased the demand for prudent risk exposure, and in this thesis we investigate regulators view on how CCPs should construct risk scenarios to meet best practice for stress testing their members’ composite portfolios. A method based on multivariate t-distributions and copula-transformations applied to historical time series data, is proposed for constructing an independent scenario generator which should be used as a compliment to other, more knowledge-based methods. The method was implemented in Matlab to test the theory in practice, and experiments were setup for pure stock portfolios as well as for derivative based portfolios. Backtests were then carried out to validate the underlying theory on historical data spanning 25 years in total. Results show that the method proposed in this thesis indeed has the potential to be a useful approach for creating stress scenarios. Its ability to render specific levels of plausibility seems to show a sufficient level of consistency with real life data, and further research is thereby justified.
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Balčiūnaitė, Rasa. "Jungčių taikymas transporto priemonių valdytojų civilinės atsakomybės privalomojo draudimo žalų modeliavimui." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20140702_190255-88041.
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Šio darbo tema yra jungčių (angl. copulas) panaudojimas ryšiams tarp daugiamačių atsitiktinių dydžių modeliuoti. Jungtis yra funkcija, kuri sujungia kelių atsitiktinių dydžių marginalinius skirstinius į bendrą daugiamatę funkciją. Jungties sąvoka pirmą kartą statistikoje įvesta 1959 m. Šiame darbe aprašomos pagrindinės jungčių savybės, keletas jungčių šeimų, išskiriant atskirą šeimą - Archimedo jungtis, taip pat priklausomumo matai tarp atsitiktinių dydžių. Vėliau tinkamos jungties pritaikymo turimam duomenų rinkiniui procedūra iliustruojama nagrinėjant transporto priemonių valdytojų civilinės atsakomybės privalomojo draudimo žalų ir išlaidų žaloms administruoti duomenis.In this Master work the concept of copulas as a tool for modeling relationships among multivariate outcomes is introduced. A copula is a function that links univariate margins to their multivariate distribution. Copulas were introduced in 1959. The literature on the statistical properties and application of copulas has been developing rapidly in recent years. In this Master work basic properties of copulas are described, then several families of copulas and relationships to measures of dependences. Later procedure for selecting the parametric family of Archimedean copulas is illustrated by using Lithuanian Motor Third Party Liability insurance data losses and expenses. For these data it is shown how to fit copulas according to nonparametric procedure which was proposed by Genest and Rivest.
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AghaKouchak, Amir. "Simulation of remotely sensed rainfall fields using copulas." Stuttgart Inst. für Wasserbau, 2010. http://d-nb.info/1000637417/34.
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Li, Jing. "Application of copulas as a new geostatistical tool." Stuttgart Inst. für Wasserbau, 2010. http://d-nb.info/1000914682/34.
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Liu, Xinjia. "Pricing of multi-name credit derivatives using copulas." Worcester, Mass. : Worcester Polytechnic Institute, 2008. http://www.wpi.edu/Pubs/ETD/Available/etd-010808-160914/.
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Professional Master's Project in partial fulfillment of the requirements for the degree of Master of Science (M.S.)--Worcester Polytechnic Institute.Keywords: first-to-default baskets; multi-name credit derivatives; copula functions. Includes bibliographical references (leaf 29 ).
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Lü, Wei, and 吕薇. "On some goodness-of-fit tests for copulas." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B47849964.
Full textAbstract:
Copulas have been known in the statistical literature for many years, and
have become useful tools in modeling dependence structure of multivariate
random variables, overcoming some of the drawbacks of the commonly-used
correlation measures. Goodness-of-fit tests for copulas play a very important
role in evaluating the suitability of a potential input copula model. In recent
years, many approaches have been proposed for constructing goodness-of-fit
tests for copula families. Among them, the so-called “blanket tests" do not
require an arbitrary data categorization or any strategic choice of weight function, smoothing parameter, kernel, and so on.
As preliminaries, some background and related results of copulas are firstly
presented. Three goodness-of-fit test statistics belonging to the blanket test
classification are then introduced. Since the asymptotic distributions of the
test statistics are very complicated, parametric bootstrap procedures are employed to approximate critical values of the test statistics under the null hypotheses. To assess the performance of the three test statistics in the low
dependence cases, simulation studies are carried out for three bivariate copula families, namely the Gumbel-Hougaard copula family, the Ali-Mikhail-Haq
copula family, and the Farlie-Gumbel-Morgenstern copula family. Specifically
the effect of low dependence on the empirical sizes and powers of the three
blanket tests under various combinations of null and alternative copula families are examined. Furthermore, to check the performance of the three tests
for higher dimensional copulas, the simulation studies are extended to some
three-dimensional copulas. Finally the three goodness-of-fit tests are applied
to two real data sets.published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy
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Nicoloutsopoulos, Dimitrios. "Parametric and Bayesian non-parametric estimation of copulas." Thesis, University College London (University of London), 2005. http://discovery.ucl.ac.uk/1445722/.
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This thesis studies parametric and non-parametric methods of cop ula estimation with special focus on the Archimedean class of copu las. The first part proposes an estimation procedure which is indepen dent of the marginal distributions and performs well for one-parame ter or two-parameter families of copulas, where traditional methods give questionable results especially for small sample sizes. In the sec ond part we follow a Bayesian methodology and represent the copula density as a random piecewise constant, function. Under the presence of some data, we set up a probability distribution over the copula density and utilize Markov Chain Monte Carlo techniques to explore that distribution. The methodology is extended to perform shape preserving estimation of a univariate convex and monotone func tion that characterizes the copula. The estimated first and second derivatives of the function of interest must satisfy the restrictions that the theory imposes. All methods are illustrated with examples from simulated samples and a real-life dataset of the daily observations of the Dow-Jones and FTSE financial indices.
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Gudmundarson, Ragnar Levi. "Ruin probability and copulas : applications in insurance pricing." Master's thesis, Instituto Superior de Economia e Gestão, 2020. http://hdl.handle.net/10400.5/20623.
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Mestrado em Actuarial ScienceNesta tese, a probabilidade de ruína do processo de risco de Lundberg é usada como um critério para determinar o carregamento do prêmio. São considerados os processos de sinistro único e agregado. O processo de reclamação agregada é composto por dois processos de reclamação homogêneos diferentes. Ambos os casos independentes e dependentes são considerados. Cópulas de Lévy são usadas para modelar a dependência. As cópulas de Lévy fornecem uma maneira elegante e flexível de modelar dependências e podem ser uma ferramenta útil ao modelar a dependência de processos de salto com aplicativos em seguro e gerenciamento de risco. A função de valor ótimo para probabilidade mínima de ruína é analisada e a teoria de controle estocástico é usada para obter o carregamento ótimo do princípio do prêmio esperado, minimizando a probabilidade de ruína. Simulações numéricas de diferentes estudos de caso são apresentadas
In this thesis ruin probability of the Lundberg risk process is used as a criterion for determining the security loading of premium. Both single and aggregated claim processes are considered. The aggregated claim process is composed of two different homogeneous claim processes. Both independent and dependent cases are considered. Lévy copulas are used to model the dependence. Lévy copulas provide an elegant and flexible manner to model dependencies and can be a useful tool when modelling dependence of jump processes with applications in insurance and risk management. The optimal value function for minimum ruin probability is analysed and stochastic control theory is used to obtain the optimal loading of the expected premium principle minimizing the probability of ruin. Numerical simulations of different case studies are presented.
info:eu-repo/semantics/publishedVersion
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Linley, Christopher. "Modelling dependance in collateralied debt obligations with copulas." Master's thesis, University of Cape Town, 2010. http://hdl.handle.net/11427/4903.
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In this paper we provide a review of credit derivatives, and some of the tools used to model them. We give a basic introduction to copulas and how they are used to model the depedence between single name credit derivatives. We then investigate various features of Gaussian and t copula dependence using numerical results obtained from Monte-Carlo simulation.
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Taku, Marie Manyi. "Modelling Dependence of Insurance Risks." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-9064.
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Modelling one-dimensional data can be performed by different wellknown ways. Modelling two-dimensional data is a more open question. There is no unique way to describe dependency of two dimensional data. In this thesis dependency is modelled by copulas. Insurance data from two different regions (Göinge and Kronoberg) in Southern Sweden is investigated. It is found that a suitable model is that marginal data are Normal Inverse Gaussian distributed and copula is a better dependence measure than the usual linear correlation together with Gaussian marginals.
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Coblenz, Maximilian [Verfasser], and O. [Akademischer Betreuer] Grothe. "Advances in Dependence Modeling: Multivariate Quantiles, Copula Level Curve Lengths, and Non-Simplified Vine Copulas / Maximilian Coblenz ; Betreuer: O. Grothe." Karlsruhe : KIT-Bibliothek, 2018. http://d-nb.info/1174252022/34.
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Santos, Mariana Faria dos. "Modelling claim counts of homogeneous risk groups using copulas." Master's thesis, Instituto Superior de Economia e Gestão, 2010. http://hdl.handle.net/10400.5/2932.
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Mestrado em Ciências ActuariaisOver the years modelling the dependence between random variables has been a challenge in many areas, like insurance and finance. Recently with the new capital requirement regime for the European insurance business, this subject is increasing importance since, according to Solvency II, the insurer's risks should be modelled separately, then aggregated follow¬ing some dependence structure. The challenge of this framework is to achieve an accurate way of joining dependent risks in order to not over or underestimate the capital require¬ments. The aim of this thesis is to give a practical application of a multivariate model based on copulas as well as all the theoretical and important concepts related to the theory of copulas. Although the definition of copula dates from 1959, only recently some authors such Clemen and Reilly (1999), Daul et al (2003), Dias (2004), Frees and Valdez (1998) and Embrechts et al (2003) applied the copula framework for the finance and insurance data. In the mean time, estimation procedures and goodness-of-fit tests has been developing in the literature. In this thesis we introduce the theory of copulas together with the study of copula models for insurance data. Beforehand, copula definition andpropertiesaswellassome types of copulas discussed in literature are introduced. We present methods to estimate the parameters and a goodness-of-fit test for copulas. Afterwards, we present a summary of Solvency II and a multivariate model to fit claim counts between three homogeneous risk groups that are the core of the automobile business: Third party liability property damages, third party liability bodily injury and material own damages. The methodology followed is based on copula models and the procedures are carried out in two steps. First, we model the marginal distributions of each risk group and test the goodness-of-fit of each distribution. We propose two models to fit the marginal distributions: a discrete and an approximating continuous model. In the first model we test a Poisson and a Negative Binomial distribution whereas in the second one we test a Gamma and a Normal distribution approximations. In spite of being the natural approach to fit the claim counts, the discrete model has some limitations since copulas have serious restrictions when the marginals are discrete. Thus, a continuous model is proposed to fit the data as an alternative avoiding these limitations. Finally, we fitdifferent copulas families estimating its parameters through some procedures, presented along this thesis. We evaluate the goodness-of-fit using a statistical test based on the empirical copula concept.
Ao longo dos últimos anos, avaliar a dependência entre variáveis aleatórias tem sido um desafio constante em muitas áreas, como por exemplo nos seguros e finanças. Recente¬mente, com o novo regime de solvência para as companhias de seguros europeias, este tema tem ganho um grande relevo, uma vez que, de acordo com o programa Solvência II, os riscos de uma companhia de seguros devem ser avaliados separadamente, sendo posteri¬ormente agregados de forma dependente. O grande desafio deste modelo é conseguir en¬contrar a forma mais correcta de agregar os diversos riscos considerando dependência, por forma a não subestimar nem sobrestimar o valor dos requisitos de capital. Posto isto, o objectivo desta tese é, por um lado, apresentar uma aplicação prática de um modelo mul-tivariado onde se utilizam diversas cópulas para avaliar a estrutura de dependência entre os riscos e, por outro lado, fornecer todos os conceitos teóricos mais importantes relacionados com a teoria das cópulas. Apesar da definição de cópula datar de 1959, apenas recente¬mente alguns autores, tais como Clemen and Reilly (1999), Daul et al (2003), Dias (2004), Frees and Valdez (1998) e Embrechts et al (2003), aplicaram este conceito à área da banca e seguros. Entretanto, têm sido desenvolvidos na literatura métodos para a estimação dos parâmetros e testes de ajustamento para modelos multivariados que utilizam cópulas. Nesta tese, a teoria das cópulas é introduzida juntamente com um estudo prático aplicado a dados de uma seguradora real. Em primeiro lugar, é apresentada a definição e as propriedades gerais das cópulas sendo também detalhadas algumas cópulas conheci¬das e estudadas na literatura. Além disto, são apresentados métodos para a estimação dos parâmetros e testes para avaliar a qualidade do ajustamento das cópulas aos dados. Segui¬damente, é feito um breve resumo sobre Solvência II e apresentado um modelo multivariado para ajustar o número de sinistros de três grupos de risco homogéneos que constituem o núcleo do ramo automóvel: Responsabilidade civil de danos materiais, responsabilidade civil de danos corporais e danos próprios. Os procedimentos são realizados em dois passos. Em primeiro lugar ajustam-se várias distribuições marginais para cada grupo de risco testando a qualidade de ajustamento de cada uma. Para o ajustamento das marginais são propostos dois modelos: um modelo discreto e um modelo de aproximação contínuo. No primeiro as distribuições testadas são a Binomial Negativa e a Poisson, enquanto que no segundo são testadas as distribuições Gama e Normal. O modelo discreto tem algumas limitações, uma vez que as cópulas têm sérias restrições quando as marginais são discretas. Daqui advém a necessidade de propor um modelo contínuo aproximado. Finalmente, ajustam-se diver¬sas cópulas utilizando métodos de estimação apresentados ao longo da tese. A qualidade do ajustamento é testada através de uma estatística tese baseada no conceito de cópula empírica.
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Maddox, Wesley J. "Dependency Measures and Copulas for Multivariate Infinitely Divisible Distributions." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1493912655994132.
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Zheng, Fei. "Learning and smoothing in switching Markov models with copulas." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC066/document.
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Les modèles de Markov à sauts (appelés JMS pour Jump Markov System) sont utilisés dans de nombreux domaines tels que la poursuite de cibles, le traitement des signaux sismiques et la finance, étant donné leur bonne capacité à modéliser des systèmes non-linéaires et non-gaussiens. De nombreux travaux ont étudié les modèles de Markov linéaires pour lesquels bien souvent la restauration de données est réalisée grâce à des méthodes d’échantillonnage statistique de type Markov Chain Monte-Carlo. Dans cette thèse, nous avons cherché des solutions alternatives aux méthodes MCMC et proposons deux originalités principales. La première a consisté à proposer un algorithme de restauration non supervisée d’un JMS particulier appelé « modèle de Markov couple à sauts conditionnellement gaussiens » (noté CGPMSM). Cet algorithme combine une méthode d’estimation des paramètres basée sur le principe Espérance-Maximisation (EM) et une méthode efficace pour lisser les données à partir des paramètres estimés. La deuxième originalité a consisté à étendre un CGPMSM spécifique appelé CGOMSM par l’introduction des copules. Ce modèle, appelé GCOMSM, permet de considérer des distributions plus générales que les distributions gaussiennes tout en conservant des méthodes de restauration optimales et rapides. Nous avons équipé ce modèle d’une méthode d’estimation des paramètres appelée GICE-LS, combinant le principe de la méthode d’estimation conditionnelle itérative généralisée et le principe des moindre-carrés linéaires. Toutes les méthodes sont évaluées sur des données simulées. En particulier, les performances de GCOMSM sont discutées au regard de modèles de Markov non-linéaires et non-gaussiens tels que la volatilité stochastique, très utilisée dans le domaine de la financeSwitching Markov Models, also called Jump Markov Systems (JMS), are widely used in many fields such as target tracking, seismic signal processing and finance, since they can approach non-Gaussian non-linear systems. A considerable amount of related work studies linear JMS in which data restoration is achieved by Markov Chain Monte-Carlo (MCMC) methods. In this dissertation, we try to find alternative restoration solution for JMS to MCMC methods. The main contribution of our work includes two parts. Firstly, an algorithm of unsupervised restoration for a recent linear JMS known as Conditionally Gaussian Pairwise Markov Switching Model (CGPMSM) is proposed. This algorithm combines a parameter estimation method named Double EM, which is based on the Expectation-Maximization (EM) principle applied twice sequentially, and an efficient approach for smoothing with estimated parameters. Secondly, we extend a specific sub-model of CGPMSM known as Conditionally Gaussian Observed Markov Switching Model (CGOMSM) to a more general one, named Generalized Conditionally Observed Markov Switching Model (GCOMSM) by introducing copulas. Comparing to CGOMSM, the proposed GCOMSM adopts inherently more flexible distributions and non-linear structures, while optimal restoration is feasible. In addition, an identification method called GICE-LS based on the Generalized Iterative Conditional Estimation (GICE) and the Least-Square (LS) principles is proposed for GCOMSM to approximate any non-Gaussian non-linear systems from their sample data set. All proposed methods are tested by simulation. Moreover, the performance of GCOMSM is discussed by application on other generable non-Gaussian non-linear Markov models, for example, on stochastic volatility models which are of great importance in finance
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Manzi, Maddalena. "New construction methods for copulas and the multivariate case." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3427458.
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Aggregation functions are mathematical objects that have the function of reducing a set of numbers into a unique representative number, combining several degrees of membership into one aggregated value. Particular kinds of aggregation functions are copulas which permit
to represent joint distribution functions by splitting the marginal behaviour, embedded in the marginal distributions, from the dependence captured by the copula itself.
The concept of copula can be extended to n dimensions, but multivariate extensions are generally not easily to
be done.
This thesis addresses and develops a new unified approach to copula-based modelling and characterizations
of aggregation functions in the multivariate case.
To cope with
this problem, we have to understand the algebraic structure of lattice and supermodularity on
a general lattice, because supermodularity is strictly connected to 2-increasingness and in the bivariate case copulas are a subclass of supermodular aggregation functions.Le funzioni di aggregazione sono strumenti matematici importanti che riducono un insieme di numeri in un unico numero rappresentativo, combinando i vari gradi di appartenenza nel valore aggregato. Importanti funzioni di aggregazione sono le copule, che permettono di rappresentare funzioni di distribuzione marginali con la funzione di distribuzione congiunta, che cattura proprio nella copula la dipendenza tra le marginali. Il concetto di copula può essere esteso al caso multidimensionale, ma costruire copule multivariate non è un problema semplice. Questa tesi, partendo dalla generalizzazione dell'assioma tipico delle copule nel caso bivariato, apre la strada alle costruzioni multivariate. Si generalizza l'assioma di supermodularità con quello di ultramodularità e l'investigazione affronta il problema con un approccio unificato, studiando le copule proprio come particolari tipi di funzioni d'aggregazione.
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Ahmed, Nasreldin Osama. "Using statistical copulas to measure dependence in the agrofood sector." Doctoral thesis, Universitat Politècnica de Catalunya, 2015. http://hdl.handle.net/10803/285931.
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This thesis has been pursued in three papers whose nexus is the use of statistical copulas for the purpose of assessing dependence in the field of agrofood economics. The first paper aims at determining how the introduction of agricultural revenue insurance contracts in Spain will affect the cost of purchasing insurance, relative to yield insurance schemes. The empirical analysis focuses on the apple and orange sectors in Spain. Statistical copulas are used to jointly model price and yield perils. Monte Carlo simulation methods are employed to simulate premium rates both under revenue and yield insurance. Results indicate that revenue insurance is likely to reduce the price of agricultural insurance in Spain, which may result in higher acceptance and demand for agricultural insurance programs.
The second paper aims to study dependence between producer and consumer prices for millet markets in Niger. Links between prices considered are assessed by cointegration analysis and statistical copula methods. Results indicate a positive link between producer and consumer prices, which is stronger the closer the markets are. Evidence of asymmetric price behavior is also found.
The last paper assesses price transmission along the Egyptian tomato food marketing chain in the period that followed the Arab Spring. Static and time-varying copula methods are used for this purpose. Results suggest a positive link between producer, wholesaler and retail tomato prices. Such positive dependence is characterized by asymmetries during extreme market events, which lead price increases to be transferred more completely along the supply chain than price declines.Esta tesis se compone de tres artículos científicos cuyo nexo de unión es el uso de copulas estadísticas para analizar dependencia en el ámbito de la economía agroalimentaria. En el primer artículo, se estudia cómo la introducción de los contratos de seguro de ingresos agrícolas en España puede afectar el coste de la contratación de un seguro, en comparación con el tradicional seguro de rendimientos agrícolas. El análisis empírico se centra en los sectores de la manzana y la naranja en España. Las cópulas estadísticas se utilizan para modelar la dependencia entre los precios y los rendimientos agrarios. Los métodos Monte Carlo se utilizan para simular del importe de las primas del seguro de ingresos y del seguro de rendimientos. Los resultados indican que es probable que el seguro de ingresos reduzca el costo de los seguros agrarios en España, lo que puede conllevar una mayor aceptación y demanda de programas de seguros agrícolas. El segundo artículo tiene como objetivo estudiar la dependencia entre los precios al productor y al consumidor en el mercado del mijo en Níger. Los vínculos entre los precios considerados son evaluados mediante un análisis de cointegración y el método estadístico de cópula. Los resultados sugieren la existencia de una relación positiva entre el precio del productor y del consumidor, la cuál aumenta cuanto más próximos se encuentren los mercados. También se han hallado evidencias de asimetría en el comportamiento de los precios. El último artículo evalúa la transmisión de precios a lo largo de la cadena de comercialización alimentaria egipcia del tomate. El estudio se centra en el período posterior a la Primavera Árabe. Métodos de copula estática y dinámica se utilizan con este propósito. Los resultados sugieren la existencia de una relación positiva entre los precios al productor, mayorista y vendedor al detalle. Esta dependencia positiva presenta asimetrías durante los eventos extremos del mercado, que conllevan que el aumento de los precios se transfiriera de manera más completa a lo largo de la cadena de suministro que las disminuciones de precio.
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Reh, Lena [Verfasser]. "Measuring Multivariate Dependence - an Analytical Approach with Copulas / Lena Reh." München : Verlag Dr. Hut, 2012. http://d-nb.info/1028785054/34.
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Xia, Xinghua. "Essays on dependence modelling with vine copulas and its applications." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42235.
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This thesis contains three essays on dependence modelling with high dimension vine copulas and its applications in credit portfolio risk, asset allocation and international financial contagion. In the first essay, we demonstrate the superiority of vine copulas over multivariate Gaussian copula when modelling the dependence structure of a credit portfolio risk factors. We introduce the vine copulas to modelling the dependence structure of multi risk factors log returns in the combined framework of both threshold model and mixture model credit risk modelling. The second essay studies asset allocation decisions in the presence of regime switching on asset allocation with alternative investments. We find evidence that two regimes, characterized as bear and bull states, are required to capture the joint distribution of stock, bond and alternative investments returns. Optimal asset allocation varies considerably across these states and changes over time. Therefore, in order to capture observed asymmetric dependence and tail dependence in financial asset returns, we introduce high dimensional vine copula and construct a multivariate vine copula regime-switching model, which account for asymmetric dependence and tail dependence in high dimensional data. The third essay explores the cross-market dependence between six popular equity indices (S&P 500, NASDAQ 100, FTSE 100, DAX 30, Euro Stoxx 50 and Nikkei 225), and their corresponding volatility indices (VIX, VXN, VFTSE, VDAX, VSTOXX and VXJ). In particular, we propose a novel dynamic method that combine the Generalised Autoregressive Score (GAS) Method with high dimension R-vine copula approach which is able to capture the time-varying tail dependence coefficient (TDC) of index returns.
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Carmo, Frederico Augusto Rosa do. "Estimativa das funções de recuperação de reservas minerais usando copulas." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/287450.
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Orientador: Armando Zaupa RemacreTese (doutorado) - Universidade Estadual de Campinas, Instituto de Geociencias
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Resumo: O objetivo principal desta tese foi desenvolver a metodologia de cópulas aplicada ao problema de estimativas de reservas condicionadas, corrigindo erros de tonelagem e quantidade de minério de um projeto, via uma abordagem diferente da simulação estocástica condicional. É apresentado um resumo teórico que fundamenta o estudo de cópulas. Inicia-se com a apresentação de definições e conceitos importantes da estatística e da probabilidade. Após uma discussão sobre medidas de correlação, é introduzido o conceito de cópulas, desde sua definição e propriedades básicas até o estudo de alguns tipos de cópulas essenciais para a aplicação nesta tese. É discutida toda a fundamentação teórica desenvolvida para o cálculo de recursos recuperáveis. Os conceitos de curvas de tonelagem e teores são introduzidos, pois são a base da parametrização de reservas minerais. É mostrado como a cópula pode ser utilizada num dos pontos principais da geoestatística mineira, principalmente no que diz respeito ao erro das estimativas. Discorre-se primeiramente sobre o conceito de validação cruzada, apresentando a definição de reserva ilusória, ótima e ideal. É definida a reserva ideal utilizando o conceito de cópulas, onde a krigagem, a simulação seqüencial gaussiana e a cópula são comparadas, mostrando as conseqüências da sobreestimativa e da subestimativa em projetos de cava e seqüenciamento na mineração
Abstract: The aim of this thesis was to develop the applied methodology of copulas in the problem of conditional reserves estimation. The copulas have a different approach from sequential gaussian simulation and in this thesis was used to correct the tonnage and ore quantity of a mining project. It is presented a theoretical summary that is the bases to the study of copulas. It is also' presented a set of definitions and important concepts of the statistics and the probability. After a discussion about correlation measures, is introducing the concept of copulas, begining with the definition and basic properties until the study of some types of essential copulas that was applied in this thesis. Whole the theoretical fundamentation is discussed to developed the calculation of recoverable resources. The concepts of tonnage and grades curves are introduced, therefore they are the base of the parametrization of mineral reserves. It is shown how the copulas can be used in the main points of the mining geostatistics, mainly in what concerns the estimation errors. Firstly the cross validation concept is presented and the illusory, best and ideal reserves are defined. The ideal reserves is defined using the concept of copulas, and the results are compared with the kriging and sequential gaussian simulation. With this comparisons is possible shown the consequences of the upper-estimation and under estimation in an open pit projects and sequential mining layout
Doutorado
Administração e Politica de Recursos Minerais
Doutor em Ciências
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Garzon, Rozo Betty Johanna. "Modelling operational risk using skew t-copulas and Bayesian inference." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/25751.
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Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. The analysis of dependence via copula models has been focussed on the bivariate case mainly. In the vast majority of instances symmetric elliptical copulas are employed to model dependence for severities. This thesis proposes a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severities, and to calculate the capital for operational risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mixture distribution (the Lognormal for the body of losses and the generalised Pareto Distribution for the tail) using a technique from extreme value theory, (ii) the multivariate skew t-copula applied for the first time across severities and (iii) Bayesian theory. The former to model severities, I test simultaneously several parametric distributions and the mixture distribution for each business line. This procedure enables me to achieve multiple combinations of the severity distribution and to find which fits most closely. The second to effectively model asymmetry and extreme dependence in high dimensions. The third to estimate the copula model, given the high multivariate component (i.e. eight business lines and seven event types) and the incorporation of mixture distributions it is highly difficult to implement maximum likelihood. Therefore, I use a Bayesian inference framework and Markov chain Monte Carlo simulation to evaluate the posterior distribution to estimate and make inferences of the parameters of the skew t-copula model. The research analyses an updated operational loss data set, SAS® Operational Risk Global Data (SAS OpRisk Global Data), to model operational risk at international financial institutions. I then evaluate the impact of this multivariate, asymmetric and extreme dependence on estimating the total regulatory capital, among other established multivariate copulas. My empirical findings are consistent with other studies reporting thin and medium-tailed loss distributions. My approach substantially outperforms symmetric elliptical copulas, demonstrating that modelling dependence via the skew t-copula provides a more efficient allocation of capital charges of up to 56% smaller than that indicated by the standard Basel model.
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Sumbhoolaul, Helina. "Estimation of value-at-risk and expected shortfall using copulas." Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4362.
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Zheng, Ming. "On the use of copulas in dependent competing risk theory." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1340808174.
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Dobric, Jadran. "Nichtparametrische Inferenz für Copulas : quantitative Risikoanalysen für den deutschen Finanzmarkt /." Aachen : Shaker, 2008. http://d-nb.info/990756920/04.
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Savu, Cornelia. "Modellierung multivariater Abhängigkeitsstrukturen auf Finanzmärkten mit archimedischen und hierarchischen archimedischen Copulas /." Berlin : Logos-Verl, 2007. http://deposit.d-nb.de/cgi-bin/dokserv?id=3004808&prov=M&dok_var=1&dok_ext=htm.
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Li, Jing [Verfasser]. "Application of copulas as a new geostatistical tool / von Jing Li." Stuttgart : Inst. für Wasserbau, 2010. http://d-nb.info/1000914682/34.
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AghaKouchak, Amir [Verfasser]. "Simulation of remotely sensed rainfall fields using copulas / von Amir AghaKouchak." Stuttgart : Inst. für Wasserbau, 2010. http://d-nb.info/1000637417/34.
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Quinn, Casey. "The Health economic applications of Copulas: methods in applied econometrics reasearch." Thesis, University of York, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.489199.
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This thesis presents copulas as a statistical methodology appropriate to applied health economic research. Like all applied economic and econometric analysis, health economics applies econometric methods under certain assumptions. I propose here that copulas be used in place of common assumptions made when analysing multivariate data, specifically the distributional and dependence assimiptions commonly made jointly-dependent outcomes in health and health care.
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Chui, Chin Man. "Essays on exponential series estimation and application of copulas in financial econometrics." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2857.
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Orrenius, Johan. "Optimal mass transport: a viable alternative to copulas in financial risk modeling?" Thesis, KTH, Matematik (Inst.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-231829.
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Copulas as a description of joint probability distributions is today common when modeling financial risk. The optimal mass transport problem also describes dependence structures, although it is not well explored. This thesis explores the dependence structures of the entropy regularized optimal mass transport problem. The basic copula properties are replicated for the optimal mass transport problem. The estimation of the parameters of the optimal mass transport problem is attempted using a maximum likelihood analogy, but only successful when observing the general tendencies on a grid of the parameters.Copulas som en beskrivning av simultanfördelning är idag en vanlig modell för finansiell risk. Optimala masstransport problemet beskriver också simultant beroende mellan fördelningar, även om det är mindre undersökt. Denna uppsats undersöker beroendestrukturer av det entropiregulariserade optimala masstransport problemet. De basala egenskaperna hos copulas är replikerade för det optimala masstransport problemet. Ett försök att skatta parametrarna i det optimala masstransport problemet görs med en maximum-likelihood liknande metod, men är endast framgångsrik i att uppsakata de generella tendenserna på en grid av parametrarna.
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Oduneye, Chris Emeka. "Credit modelling : generating spread dynamics with intensities and creating dependence with copulas." Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/6910.
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The thesis is an investigation into the pricing of credit risk under the intensity framework with a copula generating default dependence between obligors. The challenge of quantifying credit risk and the derivatives that are associated with the asset class has seen an explosion of mathematical research into the topic. As credit markets developed the modelling of credit risk on a portfolio level, under the intensity framework, was unsatisfactory in that either: 1. The state variables of the intensities were driven by diffusion processes and so could not generate the observed level of default correlation (see Schönbucher (2003a)) or, 2. When a jump component was added to the state variables, it solved the problem of low default correlation, but the model became intractable with a high number of parameters to calibrate to (see Chapovsky and Tevaras (2006)) or, 3. Use was made of the conditional independence framework (see Duffie and Garleanu (2001)). Here, conditional on a common factor, obligors’ intensities are independent. However the framework does not produce the observed level of default correlation, especially for portfolios with obligors that are dispersed in terms of credit quality. Practitioners seeking to have interpretable parameters, tractability and to reproduce observed default correlations shifted away from generating default dependence with intensities and applied copula technology to credit portfolio pricing. The one factor Gaussian copula and some natural extensions, all falling under the factor framework, became standard approaches. The factor framework is an efficient means of generating dependence between obligors. The problem with the factor framework is that it does not give a representation to the dynamics of credit risk, which arise because credit spreads evolve with time. A comprehensive framework which seeks to address these issues is developed in the thesis. The framework has four stages: 1. Choose an intensity model and calibrate the initial term structure. 2. Calibrate the variance parameter of the chosen state variable of the intensity model. 3. When extended to a portfolio of obligors choose a copula and calibrate to standard market portfolio products. 4. Combine the two modelling frameworks, copula and intensity, to produce a dynamic model that generates dependence amongst obligors. The thesis contributes to the literature in the following way: • It finds explicit analytical formula for the pricing of credit default swaptions with an intensity process that is driven by the extended Vasicek model. From this an efficient calibration routine is developed. Many works (Jamshidian (2002), Morini and Brigo (2007) and Schönbucher (2003b)) have focused on modelling credit swap spreads directly with modified versions of the Black and Scholes option formula. The drawback of using a modified Black and Scholes approach is that pricing of more exotic structures whose value depend on the term structure of credit spreads is not feasible. In addition, directly modelling credit spreads, which is required under these approaches, offers no explicit way of simulating default times. In contrast, with intensity models, there is a direct mechanism to simulate default times and a representation of the term structure of credit spreads is given. Brigo and Alfonsi (2005) and Bielecki et al. (2008) also consider intensity modelling for the purposes of pricing credit default swaptions. In their works the dynamics of the intensity process is driven by the Cox Ingersoll and Ross (CIR) model. Both works are constrained because the parameters of the CIR model they consider are constant. This means that when there is more than one tradeable credit default swaption exact calibration of the model is usually not possible. This restriction is not in place in our methodology. • The thesis develops a new method, called the loss algorithm, in order to construct the loss distribution of a portfolio of obligors. The current standard approach developed by Turc et al. (2004) requires differentiation of an interpolated curve (see Hagan and West (2006) for the difficulties of such an approach) and assumes the existence of a base correlation curve. The loss algorithm does not require the existence of a base correlation curve or differentiation of an interpolated curve to imply the portfolio loss distribution. • Schubert and Schönbucher (2001) show theoretically how to combine copula models and stochastic intensity models. In the thesis the Schubert and Schönbucher (2001)framework is implemented by combining the extended Vasicek model and the Gaussian copula model. An analysis of the impact of the parameters of the combined models and how they interact is given. This is as follows: – The analysis is performed by considering two products, securitised loans with embedded triggers and leverage credit linked notes with recourse. The two products both have dependence on two obligors, a counterparty and a reference obligor. – Default correlation is shown to impact significantly on pricing. – We establish that having large volatilities in the spread dynamics of the reference obligor or counterparty creates a de-correlating impact: the higher the volatility the lower the impact of default correlation. – The analysis is new because, classically, spread dynamics are not considered when modelling dependence between obligors. • The thesis introduces a notion called the stochastic liquidity threshold which illustrates a new way to induce intensity dynamics into the factor framework. • Finally the thesis shows that the valuation results for single obligor credit default swaptions can be extended to portfolio index swaptions after assuming losses on the portfolio occur on a discretised set and independently to the index spread level.
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Dobric, Jadran [Verfasser]. "Nichtparametrische Inferenz für Copulas: Quantitative Risikoanalysen für den deutschen Finanzmarkt / Jadran Dobric." Aachen : Shaker, 2008. http://d-nb.info/1161303855/34.
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Yang, Wen. "Drought Analysis under Climate Change by Application of Drought Indices and Copulas." PDXScholar, 2010. https://pdxscholar.library.pdx.edu/open_access_etds/716.
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Drought is a recurrent extreme climate event with tremendous hazard for every specter of natural environment and human lives. Drought analysis usually involves characterizing drought severity, duration and intensity. Similar to most of the hydrological problems, such characteristic variables are usually not independent. Copula, as a model of multivariate distribution, widely used in finance, actuarial analysis, has won increasingly popularity in hydrological study. Here, the study has two major focuses: (1) fit drought characteristics from Streamflow Drought Index (SDI) or Standardized Runoff Index (SRI) to appropriate copulas, then using fitted copulas to estimate conditional drought severity distribution and joint return periods for both historical time period 1920-2009 and future time period 2020-2090. SDI is calculated based on long term observed streamflow while SRI is based on simulated future runoff. Parameters estimation of marginal distribution and copulas are provided, with goodness fit measures as well; (2) investigate the effects of climate change on the frequency and severity of droughts. In order to quantify the impact, three drought indices have been proposed for this study to characterize the drought duration, severity and intensity changes under the climate change in Upper Klamath River Basin. Since drought can be defined as different types, such as meteorological drought, agricultural drought, hydrological drought and social economical drought, this study chooses Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI) and Surface Water Supply Index (SWSI) to estimate the meteorological, agricultural and hydrological drought, respectively. Climate change effects come from three sources: the inherent reason, the human activity and the GCMs uncertainties. Therefore, the results show the long term drought condition by calculating yearly drought indices, and compared in three ways: First, compare drought characteristics of future time periods with base period; second, show the uncertainties of three greenhouse gas emission scenarios; third, present the uncertainties of six General Circulation Models (GCMs).