Letteratura scientifica selezionata sul tema "Copules (mathématiques)"
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Tesi sul tema "Copules (mathématiques)":
Lmoudden, Aziz. "Une généralisation de la copule de Khoudraji. Copules engendrées par des fonctions complètement monotones". Thesis, Université Laval, 2011. http://www.theses.ulaval.ca/2011/28122/28122.pdf.
Romdhani, Hela. "Mesures d'association pour des modèles de copules multidimensionnelles". Thesis, Université Laval, 2013. http://www.theses.ulaval.ca/2013/29875/29875.pdf.
In this thesis we are interested in measuring the dependence under copula models. We deal with three problems: the measure of association in the bivariate case in the presence of lower detection limits, the measure of association for clustered data and the measure of association for two-level hierarchical data. The first problem, independent of the other two, deals with the measure of association between two variables subject to fixed left censoring due to the presence of lower detection limits. We define a conditional version of Kendall’s tau to measure the association between such variables. We provide a nonparametric estimator of this measure and study its asymptotic properties. We then assume an Archimedean copula model and deduce an estimator for the copula’s Kendall’s tau. A goodness-of-fit test for the assumed copula is developed. The second problem deals with the measure of intra-class association for clustered data such that observations within each group are exchangeable. For this, we introduce an exchangeable version of Kendall’s tau as a measure of intra-class dependance and provide a nonparametric estimator for this measure. Its asymptotic properties are investigated under a multivariate exchangeable copula model. We derive an estimator of the intra-class correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under a generalized oneway ANOVA model. Finally, we develop an intra-class independence test based on Kendall’s tau. The third problem is an extension of the second to the case of hierarchical data with a set of subgroups nested into groups, such that the units within each subgroup are exchangeable and the subgroups belonging to the same group are themselves exchangeable. We define two association measures based on the exchangeable Kendall’s tau and propose nonparametric estimators for these measures. We investigate their asymptotic properties under hierarchical copula models satisfying some properties of partial exchangeability. For data drawn from meta-elliptical hierarchical copulas we deduce estimators for the intra-class correlation coefficients associated to groups and subgroups respectively. We also develop procedures for testing the effects of groups and subgroups.
Totouom, Tangho Daniel. "Copules dynamiques : applications en finance & en économie". Paris, ENMP, 2007. https://pastel.archives-ouvertes.fr/pastel-00003260.
In this thesis, we show that with the growth of credit derivatives markets, new products are continually being created and market liquidity is increasing. After reviewing these products starting out from the credit default swap, CDS, and describing their evolution since their inception in the early 90s, we demonstrate that this development has been market driven, with the mathematical models used for pricing lagging behind. As the market developed, the weak points of the models became apparent and improved models had to be developed. In October 2003 when the work on this thesis started, CDOs (Collateralised Debt Obligations) were becoming standard products. A new generation of products which we will refer to as third generation credit derivatives were starting to come on line: these include forward-starting CDS, forward-starting CDOs, options on CDOs, CPDO (in full) and so forth. In contrast to early products, these derivatives require a dynamic model of the evolution of the “correlation” between the names over time, something which base correlation was not designed to do. Our objective was to develop a family of multivariate copula processes with different types of upper and lower tail dependence so as to be able to reproduce the correlation smiles/skews observed in credit derivatives in practice. We chose to work with a dynamic version of Archimedean copulas because unlike many other copulas found in the literature, they are mathematically consistent multivariate models. Chapter 2 presents two different approaches for developing these processes. The first model developed is a non-additive jump process based on a background gamma process; the second approach is based on time changed spectrally positive Levy process. The first approach is very convenient for simulations; the second approach is based on additive building blocks and hence is a more general. Two applications of these models to credit risk derivatives were carried out. The first one on pricing synthetic CDOs at different maturities (Chapter 5) was presented at the 5th Annual Advances in Econometrics Conference in Baton Rouge, Louisiane, November 3-5 2006 and has been submitted for publication. The second one which presents a comparison of the pricing given by these dynamic copulas with five well-known copula models, has been submitted to the Journal of Derivatives (see Chapter 6). Having tested the basic dynamic copula models in a credit derivative context, we went on to combine this framework with matrix migration approach (Chapter 3). In order to market structured credit derivatives, banks have to get them rated by rating agencies such as S&P, Moody’s and Fitch. A key question is the evolution of the rating over time (i. E. Its migration). As the latest innovations in the credit derivatives markets such as Constant Proportion Debt Obligation (CPDO) require being able to model credit migration and correlation in order to handle substitutions on the index during the roll, we propose a model for the joint dynamics of credit ratings of several firms. We then proposed a mathematical framework were individual credit ratings are modelled by a continuous time Markov chain, and their joint dynamics are modelled using a copula process. Copulas allow us to incorporate our knowledge of single name credit migration processes, into a multivariate framework. This is further extended with the multi-factor and time changed approach. A multifactor approach is developed within the new formulated dynamic copula processes, and a time changed Levy process is used to introduce dependency on spread dynamics
Bourdeau-Brien, Michaël. "Les copules en finance : analyse qualitative et quantitative de l'expansion de cette théorie". Master's thesis, Université Laval, 2007. http://hdl.handle.net/20.500.11794/19266.
Desbois-Bédard, Laurence. "Génération de données synthétiques pour des variables continues : étude de différentes méthodes utilisant les copules". Master's thesis, Université Laval, 2017. http://hdl.handle.net/20.500.11794/27748.
Statistical agencies face a growing demand for releasing microdata to the public. To this end, many techniques have been proposed for publishing microdata while providing confidentiality : synthetic data generation in particular. This thesis focuses on such technique by presenting two existing methods, GAPD and C-GADP, as well as suggesting one based on vine copula models. GADP assumes that the variables of original and synthetic data are normally distributed, while C-GADP assumes that they have a normal copula distribution. Vine copula models are proposed due to their flexibility. These three methods are then assessed according to utility and risk. Data utility depends on maintaining certain similarities between the original and confidential data, while risk can be observed in two types : reidentification and inference. This work will focus on the utility examined with different analysis-specific measures, a global measure based on propensity scores and the risk of inference evaluated with a distance-based prediction.
Ben, Ghorbal Noomen. "Étude de certaines mesures d'association multivariées et d'un test de dépendance extrémale fondés sur les rangs". Thesis, Université Laval, 2010. http://www.theses.ulaval.ca/2010/27602/27602.pdf.
Marri, Fouad. "Évaluation des mesures de ruine dans le cadre de modèles avancés de risque". Thesis, Université Laval, 2009. http://www.theses.ulaval.ca/2009/26001/26001.pdf.
Cuberos, Andres. "Modélisation de la dépendance et estimation du risque agrégé". Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10321/document.
This 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
Chicheportiche, Rémy. "Dépendances non linéaires en finance". Phd thesis, Ecole Centrale Paris, 2013. http://tel.archives-ouvertes.fr/tel-01003349.
Veilleux, Dery. "Modèles de dépendance avec copule Archimédienne : fondements basés sur la construction par mélange, méthodes de calcul et applications". Master's thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/33039.
The law of large numbers, which states that statistical characteristics of a random sample will converge to the characteristics of the whole population, is the foundation of the insurance industry. Insurance companies rely on this principle to evaluate the risk of insured events. However, when we introduce dependencies between each component of the random sample, it may drastically affect the overall risk profile of the sample in comparison to the whole population. This is why it is essential to consider the effect of dependency when aggregating insurance risks from which stems the interest given to dependence modeling in actuarial science. In this thesis, we study dependence modeling in a portfolio of risks for which a mixture random variable (rv) introduces dependency. After introducing the use of exponential mixtures in actuarial risk modeling, we show how this mixture construction can define Archimedean copulas, a powerful tool for dependence modeling. First, we demonstrate how an Archimedean copula constructed via a continuous mixture can be approximated with a copula constructed by discrete mixture. Then, we derive explicit expressions for a few quantities related to the aggregated risk. The common mixture representation of Archimedean copulas is then at the basis of a computational strategy proposed to compute the distribution of the sum of risks in a general setup. Such results are then used to investigate risk models with respect to aggregation, capital allocation and ruin problems. Finally, we discuss an extension to nested Archimedean copulas, a general case of dependency via common mixture including different levels of dependency.
Résumé en espagnol
Libri sul tema "Copules (mathématiques)":
Joe, Harry. Dependence modeling with copulas. Boca Raton: CRC Press, Taylor & Francis Group, 2015.
Cherubini, Umberto. Dynamic copula methods in finance. Hoboken, NJ: Wiley, 2011.
Fusai, Gianluca. Implementing models in quantitative finance: Methods and cases. Berlin: Springer, 2008.
Durante, Fabrizio, e Carlo Sempi. Copulas: Theory and Applications. CRC Press LLC, 2015.
Joe, Harry. Dependence Modeling with Copulas. Taylor & Francis Group, 2014.
Joe, Harry. Dependence Modeling with Copulas. Taylor & Francis Group, 2014.
Joe, Harry. Dependence Modeling with Copulas. Taylor & Francis Group, 2023.
Mulinacci, Prof Sabrina, Umberto Cherubini, Sabrina Mulinacci, Fabio Gobbi e Silvia Romagnoli. Dynamic Copula Methods in Finance. Wiley & Sons, Incorporated, John, 2011.
Cherubini, Umberto, Sabrina Mulinacci, Fabio Gobbi e Silvia Romagnoli. Dynamic Copula Methods in Finance. Wiley & Sons, Limited, John, 2012.
Cherubini, Umberto, Sabrina Mulinacci, Fabio Gobbi e Silvia Romagnoli. Dynamic Copula Methods in Finance. Wiley & Sons, Incorporated, John, 2011.