Dissertations / Theses: 'Brownian motion processes'

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Dunkel, Jörn. "Relativistic Brownian motion and diffusion processes." kostenfrei, 2008. http://d-nb.info/991318757/34.

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Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.

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The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.

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Keprta, S. "Integral tests for Brownian motion and some related processes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ26856.pdf.

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Keprta, Stanislav Carleton University Dissertation Mathematics and Statistics. "Integral tests for Brownian motion and some related processes." Ottawa, 1997.

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5

Cakir, Rasit Grigolini Paolo. "Fractional Brownian motion and dynamic approach to complexity." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3992.

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6

Simon, Matthieu. "Markov-modulated processes: Brownian motions, option pricing and epidemics." Doctoral thesis, Universite Libre de Bruxelles, 2017. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/250010.

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This thesis is devoted to the study of different stochastic processes which have a common feature: they are Markov-modulated, which means that their evolution rules depend on the state occupied by an underlying Markov process. In the first part of this thesis, we analyse the stationary distribution and various first passage problems for Markov-modulated Brownian motions (MMBMs) as well as for two extensions: MMBMs with jumps and MMBMs modified by a temporary change of regime upon visits to level zero. The second part of this thesis is devoted to the use of Markov-modulated processes in mathematical finance, more precisely for the calculation of different option prices. We use a Fourier transform approach to price different European options (vanilla, exchange and quanto options) in the case where the value of the considered risky assets evolves like the exponential of a Markov-modulated Lévy process. The third part of this thesis is devoted to the study of some stochastic epidemic processes, namely the SIR processes. In our models, a Markov process is used to modulate the behaviour of the individuals who bring the disease. We use different martingale approaches as well as matrix analytic methods to obtain various information about the state of the population when the epidemic is over.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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莊競誠 and King-sing Chong. "Explorations in Markov processes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235682.

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Chong, King-sing. "Explorations in Markov processes /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18736105.

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9

Duncan, Thomas. "Brownian Motion: A Study of Its Theory and Applications." Thesis, Boston College, 2007. http://hdl.handle.net/2345/505.

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Thesis advisor: Nancy Rallis
The theory of Brownian motion is an integral part of statistics and probability, and it also has some of the most diverse applications found in any topic in mathematics. With extensions into fields as vast and different as economics, physics, and management science, Brownian motion has become one of the most studied mathematical phenomena of the late twentieth and early twenty-first centuries. Today, Brownian motion is mostly understood as a type of mathematical process called a stochastic process. The word "stochastic" actually stems from the Greek word for "I guess," implying that stochastic processes tend to produce uncertain results, and Brownian motion is no exception to this, though with the right models, probabilities can be assigned to certain outcomes and we can begin to understand these complicated processes. This work reaches to attain this goal with regard to Brownian motion, and in addition it explores several applications found in the aforementioned fields and beyond
Thesis (BA) — Boston College, 2007
Submitted to: Boston College. College of Arts and Sciences
Discipline: Mathematics
Discipline: College Honors Program

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Hult, Henrik. "Topics on fractional Brownian motion and regular variation for stochastic processes." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3604.

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The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived.

The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittles approach is applied to derive anestimator for all unknown parameters.

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Hartung, Lisa Bärbel [Verfasser]. "Extremal Processes in Branching Brownian Motion and Friends / Lisa Bärbel Hartung." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1113688432/34.

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Overbeck, Ludger. "Konditionierungen der Super-Brownsche-Bewegung und verzweigender Diffusionen." Bonn : [s.n.], 1992. http://catalog.hathitrust.org/api/volumes/oclc/29044483.html.

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Cakir, Rasit. "Fractional Brownian motion and dynamic approach to complexity." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3992/.

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The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is well known that the recrossing times of the origin by an ordinary 1D diffusion trajectory generates a distribution of time distances between two consecutive origin recrossing times with an inverse power law with index m=1.5. However, with theoretical and numerical arguments, it is proved that this is the special case of a more general condition, insofar as the recrossing times produced by the dynamic FBM generates process with m=2-H. Later, the model of ballistic deposition is studied, which is as a simple way to establish cooperation among the columns of a growing surface, to show that cooperation generates memory properties and, at same time, non-Poisson renewal events. Finally, the connection between trajectory and density memory is discussed, showing that the trajectory memory does not necessarily yields density memory, and density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory.

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Erdogan, Ahmet Yasin. "Analysis of the effects of phase noise and frequency offest in orthogonal frequency division multiplexing (OFDM) systems /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Mar%5FErdogan.pdf.

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Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2004.
Thesis advisor(s): Murali Tummala, Roberto Cristi. Includes bibliographical references (p. 127-129). Also available online.

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Lappala, Anna. "Molecular dynamics simulations : from Brownian ratchets to polymers." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709251.

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Sanyal, Suman. "Stochastic dynamic equations." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Sanyal_09007dcc80519030.pdf.

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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.
Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 21, 2008) Includes bibliographical references (p. 124-131).

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Maher, David Graham School of Mathematics UNSW. "Brownian motion and heat kernels on compact lie groups and symmetric spaces." Awarded by:University of New South Wales. School of Mathematics, 2006. http://handle.unsw.edu.au/1959.4/28295.

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An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and ildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It??o type stochastic differential equations and applying the Feynman-Ka??c theorem. We also consider wrapping Brownian motion to various symmetric spaces, where a global generalisation of Rouvi`ere???s formula and the e-function are considered. Additionally, we extend some of our results to complex Lie groups, and certain non-compact symmetric spaces.

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Wu, Tung-Lung Jr. "Linear and non-linear boundary crossing probabilities for Brownian motion and related processes." Applied Probability Trust - Journal of Applied Probability, 2010. http://hdl.handle.net/1993/8123.

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We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

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Tanner, Stephen. "Non-tangential and conditioned Brownian convergence of pluriharmonic functions /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5729.

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Bessada, Dennis Fernandes Alves. "Generalizações do movimento browniano e suas aplicações à física e a finanças /." São Paulo : [s.n.], 2005. http://hdl.handle.net/11449/91854.

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Orientador: Gerson Francisco
Banca: Victo dos Santos Filho
Banca: Fernando Manoel Ramos
Resumo: Realizamos neste trabalho uma exposição geral da Teoria do Movimento Browniano, desde suas primeiras observações, feitas no âmbito da Biologia, até sua completa descrição seundo as leis da Mecânica estatística, formulação esta efetuada por Einstein em 1905. Com base nestes princípios físicos analisamos a Teoria do Movimento Browniano de Einstein como sendo um processo estocástico, o que permite sua generalização para um processo de Lévy. Fazemos uma exposição da Teoria de Lévy, e aplicamo-la em seguida na análise de dados provenientes do índice IBOVESPA. Camparamos os resultados com as distribuições empíricas e a modelada via distribuição gaussiana, demonstrando efetivamente que a série financeira analisada apresenta um comportamento não-gaussiano.
Abstracts: We review in this work the foundations of the Theory of Brownian Motion, from the first observations made in Biology to its complete description according to the laws of Statistical Mechanics performed by einstein in 1905. Afterwards we discuss the Einstein's Theory of Brownian Motion as a stochastic process, since this connection allows its generalization to a Lévy process. After a brief review of Lévy Theory we analyse IBOVESPA data within this framework. We compare the outcomes with the empirical and gaussian distributions, showing effectively that the analyzed financial series behaves exactly as a non-gaussian stochastic process.
Mestre

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Nouri, Suhila Lynn. "Expected maximum drawdowns under constant and stochastic volatility." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-050406-151319/.

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Swanson, Jason. "Variations of stochastic processes : alternative approaches /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5733.

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Bessada, Dennis Fernandes Alves [UNESP]. "Generalizações do movimento browniano e suas aplicações à física e a finanças." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/91854.

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Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-04Bitstream added on 2014-06-13T20:48:05Z : No. of bitstreams: 1 bessada_dfa_me_ift.pdf: 3052096 bytes, checksum: bfe2b25d2283cf5ec06ca7dc7407c70c (MD5)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Realizamos neste trabalho uma exposição geral da Teoria do Movimento Browniano, desde suas primeiras observações, feitas no âmbito da Biologia, até sua completa descrição seundo as leis da Mecânica estatística, formulação esta efetuada por Einstein em 1905. Com base nestes princípios físicos analisamos a Teoria do Movimento Browniano de Einstein como sendo um processo estocástico, o que permite sua generalização para um processo de Lévy. Fazemos uma exposição da Teoria de Lévy, e aplicamo-la em seguida na análise de dados provenientes do índice IBOVESPA. Camparamos os resultados com as distribuições empíricas e a modelada via distribuição gaussiana, demonstrando efetivamente que a série financeira analisada apresenta um comportamento não-gaussiano.
Abstracts: We review in this work the foundations of the Theory of Brownian Motion, from the first observations made in Biology to its complete description according to the laws of Statistical Mechanics performed by einstein in 1905. Afterwards we discuss the Einstein's Theory of Brownian Motion as a stochastic process, since this connection allows its generalization to a Lévy process. After a brief review of Lévy Theory we analyse IBOVESPA data within this framework. We compare the outcomes with the empirical and gaussian distributions, showing effectively that the analyzed financial series behaves exactly as a non-gaussian stochastic process.

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Corry, Ben Alexander. "Simulation studies of biological ion channels." View thesis entry in Australian Digital Theses Program, 2002. http://thesis.anu.edu.au/public/adt-ANU20030423.162927/index.html.

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Lyons, Simon. "Inference and parameter estimation for diffusion processes." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10518.

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Diffusion processes provide a natural way of modelling a variety of physical and economic phenomena. It is often the case that one is unable to observe a diffusion process directly, and must instead rely on noisy observations that are discretely spaced in time. Given these discrete, noisy observations, one is faced with the task of inferring properties of the underlying diffusion process. For example, one might be interested in inferring the current state of the process given observations up to the present time (this is known as the filtering problem). Alternatively, one might wish to infer parameters governing the time evolution the diffusion process. In general, one cannot apply Bayes’ theorem directly, since the transition density of a general nonlinear diffusion is not computationally tractable. In this thesis, we investigate a novel method of simplifying the problem. The stochastic differential equation that describes the diffusion process is replaced with a simpler ordinary differential equation, which has a random driving noise that approximates Brownian motion. We show how one can exploit this approximation to improve on standard methods for inferring properties of nonlinear diffusion processes.

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Vardar, Ceren. "On the Correlation of Maximum Loss and Maximum Gain of Stock Price Processes." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1224274306.

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Ufuktepe, Ünal. "Positive solutions of nonlinear elliptic equations in the Euclidean plane /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9841364.

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Osborn, Allan Ray. "Flow control methods in a high-speed virtual channel." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/13521.

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Zhou, Wei, and 周硙. "Topics in optimal stopping with applications in mathematical finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46582046.

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Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.

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Thesis (MSc)--Stellenbosch University, 2015
ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian motion setup is presented. When modelling LIBOR rates the use of a more realistic driving process is important since these rates are the most realistic interest rates used in the market of financial trading on a daily basis. Since the financial crisis there has been an increasing demand and need for efficient modelling and management of risk within the market. This has further led to the motivation of the use of Lévy based models for the modelling of credit risky financial instruments. The motivation stems from the basic properties of stationary and independent increments of Lévy processes. With these properties, the model is able to better account for any unexpected behaviour within the market, usually referred to as "jumps". Taking both of these factors into account, there is much motivation for the construction of a model driven by Lévy processes which is able to model credit risk and credit risky instruments. The model for LIBOR rates driven by these processes was first introduced by Eberlein and Özkan (2005) and is known as the Lévy-LIBOR model. In order to account for the credit risk in the market, the Lévy-LIBOR model with default risk was constructed. This was initially done by Kluge (2005) and then formally introduced in the paper by Eberlein et al. (2006). This thesis aims to present the theoretical construction of the model as done in the above mentioned references. The construction includes the consideration of recovery rates associated to the default event as well as a pricing formula for some popular credit derivatives.
AFRIKAANSE OPSOMMING : In onlangse jare, is die gebruik van Lévy-prosesse as ’n modellerings instrument baie meer gunstig gevind as die gebruik van die klassieke Brownse bewegingsproses opstel. Die rede hiervoor is dat hierdie prosesse meer buigsaamheid verskaf en die dinamiek van die model wat die praktyk beskryf, beter hierin vervat word. Dus is die gebruik van Lévy-prosesse vir finansiële modellering ’n motiverende faktor vir hierdie navorsingsaanbieding. As beginput word ’n raamwerk vir die LIBOR mark model met dinamika, gedryf deur ’n Lévy-proses in plaas van die klassieke Brownse bewegings opstel, aangebied. Wanneer LIBOR-koerse gemodelleer word is die gebruik van ’n meer realistiese proses belangriker aangesien hierdie koerse die mees realistiese koerse is wat in die finansiële mark op ’n daaglikse basis gebruik word. Sedert die finansiële krisis was daar ’n toenemende aanvraag en behoefte aan doeltreffende modellering en die bestaan van risiko binne die mark. Dit het verder gelei tot die motivering van Lévy-gebaseerde modelle vir die modellering van finansiële instrumente wat in die besonder aan kridietrisiko onderhewig is. Die motivering spruit uit die basiese eienskappe van stasionêre en onafhanklike inkremente van Lévy-prosesse. Met hierdie eienskappe is die model in staat om enige onverwagte gedrag (bekend as spronge) vas te vang. Deur hierdie faktore in ag te neem, is daar genoeg motivering vir die bou van ’n model gedryf deur Lévy-prosesse wat in staat is om kredietrisiko en instrumente onderhewig hieraan te modelleer. Die model vir LIBOR-koerse gedryf deur hierdie prosesse was oorspronklik bekendgestel deur Eberlein and Özkan (2005) en staan beken as die Lévy-LIBOR model. Om die kredietrisiko in die mark te akkommodeer word die Lévy-LIBOR model met "default risk" gekonstrueer. Dit was aanvanklik deur Kluge (2005) gedoen en formeel in die artikel bekendgestel deur Eberlein et al. (2006). Die doel van hierdie tesis is om die teoretiese konstruksie van die model aan te bied soos gedoen in die bogenoemde verwysings. Die konstruksie sluit ondermeer in die terugkrygingskoers wat met die wanbetaling geassosieer word, sowel as ’n prysingsformule vir ’n paar bekende krediet afgeleide instrumente.

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Al-Talibi, Haidar. "On the Relevance of Fractional Gaussian Processes for Analysing Financial Markets." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1762.

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In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.

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Long, Brian Russell. "Transport of polymers and particles in microfabricated array devices /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2008. http://hdl.handle.net/1794/8289.

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Thesis (Ph. D.)--University of Oregon, 2008.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 122-127). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

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Delorme, Mathieu. "Processus stochastiques et systèmes désordonnés : autour du mouvement Brownien." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE058/document.

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Dans cette thèse, on étudie des processus stochastiques issus de la physique statistique. Le mouvement Brownien fractionnaire, objet central des premiers chapitres, généralise le mouvement Brownien aux cas où la mémoire est importante pour la dynamique. Ces effets de mémoire apparaissent par exemple dans les systèmes complexes et la diffusion anormale. L’absence de la propriété de Markov rend difficile l’étude probabiliste du processus. On développe une approche perturbative autour du mouvement Brownien pour obtenir de nouveaux résultats, sur des observables liées aux statistiques des extrêmes. En plus de leurs applications physiques, on explore les liens de ces résultats avec des objets mathématiques, comme les lois de Lévy et la constante de Pickands
In this thesis, we study stochastic processes appearing in different areas of statistical physics: Firstly, fractional Brownian motion is a generalization of the well-known Brownian motion to include memory. Memory effects appear for example in complex systems and anomalous diffusion, and are difficult to treat analytically, due to the absence of the Markov property. We develop a perturbative expansion around standard Brownian motion to obtain new results for this case. We focus on observables related to extreme-value statistics, with links to mathematical objects: Levy’s arcsine laws and Pickands’ constant. Secondly, the model of elastic interfaces in disordered media is investigated. We consider the case of a Brownian random disorder force. We study avalanches, i.e. the response of the system to a kick, for which several distributions of observables are calculated analytically. To do so, the initial stochastic equation is solved using a deterministic non-linear instanton equation. Avalanche observables are characterized by power-law distributions at small-scale with universal exponents, for which we give new results

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Baumgarten, Christoph [Verfasser], and Frank [Akademischer Betreuer] Aurzada. "Persistence of sums of independent random variables, iterated processes and fractional Brownian motion / Christoph Baumgarten. Betreuer: Frank Aurzada." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1035276445/34.

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Herdiana, Ratna. "Numerical methods for SDEs - with variable stepsize implementation /." [St. Lucia, Qld.], 2003. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17638.pdf.

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Benjamin, Ronald. "Stochastic energetics of the Büttiker-Landauer motor and refrigerator." Birmingham, Ala. : University of Alabama at Birmingham, 2008. https://www.mhsl.uab.edu/dt/2008p/benjamin.pdf.

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Thesis (Ph. D.)--University of Alabama at Birmingham, 2008.
Additional advisors: Renato Camata, Nikolai Chernov, Perry A. Gerkines, Gunter Stolz. Description based on contents viewed Feb. 9, 2009; title from PDF t.p. Includes bibliographical references (p. 123-129).

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Arikan, Ali Ferda. "Structural models for the pricing of corporate securities and financial synergies : applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.

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Mergers are the combining of two or more firms to create synergies. These synergies may come from various sources such as operational synergies come from economies of scale or financial synergies come from increased value of securities of the firm. There are vast amount of studies analysing operational synergies of mergers. This study analyses the financial ones. This way the dynamics of purely financial synergies can be revealed. Purely financial synergies can be transformed into financial instruments such as securitization. While analysing financial synergies the puzzle of distribution of financial synergies between claimholders is investigated. Previous literature on mergers showed that bondholders may gain more than existing shareholders of the merging firms. This may become rather controversial. A merger may be synergistic but it does not necessarily mean that shareholders' wealth will increase. Managers and/or shareholders are the parties making the merger decision. If managers are acting to the best interest of shareholders then they would try to increase shareholders' wealth. To solve this problem first the dynamics of mergers were analysed and then new strategies developed and demonstrated to transfer the financial synergies to the shareholders.

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Arikan, Ali F. "Structural models for the pricing of corporate securities and financial synergies. Applications with stochastic processes including arithmetic Brownian motion." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/5416.

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Mergers are the combining of two or more firms to create synergies. These synergies may come from various sources such as operational synergies come from economies of scale or financial synergies come from increased value of securities of the firm. There are vast amount of studies analysing operational synergies of mergers. This study analyses the financial ones. This way the dynamics of purely financial synergies can be revealed. Purely financial synergies can be transformed into financial instruments such as securitization. While analysing financial synergies the puzzle of distribution of financial synergies between claimholders is investigated. Previous literature on mergers showed that bondholders may gain more than existing shareholders of the merging firms. This may become rather controversial. A merger may be synergistic but it does not necessarily mean that shareholders¿ wealth will increase. Managers and/or shareholders are the parties making the merger decision. If managers are acting to the best interest of shareholders then they would try to increase shareholders¿ wealth. To solve this problem first the dynamics of mergers were analysed and then new strategies developed and demonstrated to transfer the financial synergies to the shareholders.

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39

Suzuki, Kohei. "Convergence of stochastic processes on varying metric spaces." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215281.

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40

Gomez-Solano, Juan Rubén. "Nonequilibrium fluctuations of a Brownian particle." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00680302.

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This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.

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41

Serrano, Francisco de Castilho Monteiro Gil. "Fractional processes: an application to finance." Master's thesis, Instituto Superior de Economia e Gestão, 2016. http://hdl.handle.net/10400.5/13002.

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Mestrado em Matemática Financeira
Neste trabalho é apresentada uma extensa descrição matemática, orientada para a modelação financeira, de três principais processos fracionários: o processo Browniano fracionário e os dois processos de Lévy fracionários. Mostram-se como estes processos podem ser originados. É explorado o conceito de auto-semelhança e apresentamos algumas noções de cálculo fracionário. Também é discutido o lugar destes processos no problema de encontrar o preço de derivados financeiros e apresentamos uma nova abordagem para a simulação do processo de Lévy fracionário que permite um método Monte Carlo para encontrar o preço de derivados financeiros.
In this work it is presented an extensive mathematical description oriented to financial modelling based on three main fractional processes: the fractional Brownian motion and both fractional Lévy processes. It is shown how these processes were originated. The concept of self-similarity is explored and we present some notions of fractional calculus. It is discussed the opportunity of these processes in pricing financial derivatives and we present a new approach for simulation of the fractional Lévy process, which allows a Monte Carlo method for pricing financial derivatives.
info:eu-repo/semantics/publishedVersion

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42

Lee, Joongsup. "New control charts for monitoring univariate autocorrelated processes and high-dimensional profiles." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42711.

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In this thesis, we first investigate the use of automated variance estimators in distribution-free statistical process control (SPC) charts for univariate autocorrelated processes. We introduce two variance estimators---the standardized time series overlapping area estimator and the so-called quick-and-dirty autoregressive estimator---that can be obtained from a training data set and used effectively with distribution-free SPC charts when those charts are applied to processes exhibiting nonnormal responses or correlation between successive responses. In particular, we incorporate the two estimators into DFTC-VE, a new distribution-free tabular CUSUM chart developed for autocorrelated processes; and we compare its performance with other state-of-the-art distribution-free SPC charts. Using either of the two variance estimators, the DFTC-VE outperforms its competitors in terms of both in-control and out-of-control average run lengths when all the competing procedures are tested on the same set of independently sampled realizations of selected autocorrelated processes with normal or nonnormal noise components. Next, we develop WDFTC, a wavelet-based distribution-free CUSUM chart for detecting shifts in the mean of a high-dimensional profile with noisy components that may exhibit nonnormality, variance heterogeneity, or correlation between profile components. A profile describes the relationship between a selected quality characteristic and an input (design) variable over the experimental region. Exploiting a discrete wavelet transform (DWT) of the mean in-control profile, WDFTC selects a reduced-dimension vector of the associated DWT components from which the mean in-control profile can be approximated with minimal weighted relative reconstruction error. Based on randomly sampled Phase I (in-control) profiles, the covariance matrix of the corresponding reduced-dimension DWT vectors is estimated using a matrix-regularization method; then the DWT vectors are aggregated (batched) so that the nonoverlapping batch means of the reduced-dimension DWT vectors have manageable covariances. To monitor shifts in the mean profile during Phase II operation, WDFTC computes a Hotelling's T-square--type statistic from successive nonoverlapping batch means and applies a CUSUM procedure to those statistics, where the associated control limits are evaluated analytically from the Phase I data. We compare WDFTC with other state-of-the-art profile-monitoring charts using both normal and nonnormal noise components having homogeneous or heterogenous variances as well as independent or correlated components; and we show that WDFTC performs well, especially for local shifts of small to medium size, in terms of both in-control and out-of-control average run lengths.

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43

Popovic, Ray. "Parameter estimation error: a cautionary tale in computational finance." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34731.

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We quantify the effects on contingent claim valuation of using an estimator for the volatility of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After substituting into the GBM the direct volatility estimator for the true, but unknown, value of the parameter sigma, we derive the resulting marginal distribution of the approximated GBM. This allows us to derive post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with the basic properties of the underlying risk-neutral process. Next we extend our work to the contingent claim sensitivities associated with an assortment of European option portfolios that are based on the direct estimator of the volatility of the GBM process. Our approach to the option sensitivities - the Greeks - uses the likelihood function technique. This allows us to obtain computable results for the technically more-complicated formulae associated with our post-estimation process. We discuss an assortment of difficulties that can ensue when failing to account for estimation risk in valuation and hedging formulae.

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44

Antonini, Claudia. "Folded Variance Estimators for Stationary Time Series." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6931.

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This thesis is concerned with simulation output analysis. In particular, we are inter- ested in estimating the variance parameter of a steady-state output process. The estimation of the variance parameter has immediate applications in problems involving (i) the precision of the sample mean as a point estimator for the steady-state mean and #956;X, and (ii) confidence intervals for and #956;X. The thesis focuses on new variance estimators arising from Schrubens method of standardized time series (STS). The main idea behind STS is to let such series converge to Brownian bridge processes; then their properties are used to derive estimators for the variance parameter. Following an idea from Shorack and Wellner, we study different levels of folded Brownian bridges. A folded Brownian bridge is obtained from the standard Brownian bridge process by folding it down the middle and then stretching it so that it spans the interval [0,1]. We formulate the folded STS, and deduce a simplified expression for it. Similarly, we define the weighted area under the folded Brownian bridge, and we obtain its asymptotic properties and distribution. We study the square of the weighted area under the folded STS (known as the folded area estimator ) and the weighted area under the square of the folded STS (known as the folded Cram??von Mises, or CvM, estimator) as estimators of the variance parameter of a stationary time series. In order to obtain results on the bias of the estimators, we provide a complete finite-sample analysis based on the mean-square error of the given estimators. Weights yielding first-order unbiased estimators are found in the area and CvM cases. Finally, we perform Monte Carlo simulations to test the efficacy of the new estimators on a test bed of stationary stochastic processes, including the first-order moving average and autoregressive processes and the waiting time process in a single-server Markovian queuing system.

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45

Misiran, Masnita. "Modeling and pricing financial assets under long memory processes." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/2549.

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An important research area in financial mathematics is the study of long memory phenomenon in financial data. Long memory had been known long before suitable stochastic models were developed. Fractional Brownian motion (FBM) can be used to characterize this phenomenon. This thesis examines the use of FBM and its long memory parameter H, from the view point of estimation method, approximation, and numerical performance.How to estimate the long memory parameter H is important in financial pricing. This thesis starts by reviewing the performance of some existing preliminary methods for estimating H. It is then applied to some Malaysia financial data. Although these methods are easy to use, their performance are in doubts, in particular these methods can only get an estimator of H, without providing the dynamic, long-memory behaviour of financial price process.This thesis is therefore concerned with the estimation of the dynamic, long-memory behaviour of financial processes. We propose estimation methods based on models of two stochastic differential equations (SDEs) perturbed by FBM, that play important role in option pricing and interest rate modelling. These models are the geometric fractional Brownian motion (GFBM) and the fractional Ornstein-Uhlenbeck (FOU) model, respectively. These methods are able to obtain H and other parameters involved in the models. The efficiency of these methods are investigated through simulation study. We applied the new methods to some financial problems.We also extend this study to filtering the SDE driven by FBM in multidimensional case. We propose a novel approximation scheme to this problem. The convergence property is also established. The performance of this method is evaluated through solving some numerical examples. Results demonstrate that methods developed in this thesis are applicable and have advantages when compared with other existing approaches.

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46

Schmid, Patrick. "Random processes in truncated and ordinary Weyl chambers." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-66394.

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The work consists of two parts. In the first part which is concerned with random walks, we construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob h-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an h-transform in the Weyl chamber of type C. In the second part which is concerned with Brownian motion, we examine the non-exit probability of a multidimensional Brownian motion from a growing truncated Weyl chamber. Different regimes are identified according to the growth speed, ranging from polynomial decay over stretched-exponential to exponential decay. Furthermore we derive associated large deviation principles for the empirical measure of the properly rescaled and transformed Brownian motion as the dimension grows to infinity. Our main tool is an explicit eigenvalue expansion for the transition probabilities before exiting the truncated Weyl chamber.

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47

Duhalde, Jean-Pierre. "Sur des propriétés fractales et trajectorielles de processus de branchement continus." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066029/document.

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Cette thèse étudie certaines propriétés fractales et trajectorielles de processus de branchement en temps et espace continus. De façon informelle, ce type de processus est obtenu en considérant l'évolution d'une population où les individus se reproduisent et meurent au cours du temps, et ce de manière aléatoire. Le premier chapitre concerne la classe des processus de branchement avec immigration. On donne une formule semi-explicite pour la transformée de Laplace des temps d'atteinte ainsi qu'une condition nécessaire et suffisante de récurrence-transience. Ces deux résultats illustrent la compétition branchement/immigration. Le second chapitre considère l'arbre Brownien et ses mesures de temps local, dites mesures de niveau. On montre que celles-ci s'obtiennent comme restriction, à une constante près explicitée, d'une certaine mesure de Hausdorff sur l'arbre. Le résultat est montré simultanément pour tous niveaux. Le troisième chapitre étudie le Super-mouvement Brownien associé à un mécanisme de branchement général. Sa mesure d'occupation totale est obtenue comme restriction d'une certaine mesure de packing dans l'espace euclidien. Le résultat est valable en grande dimension. La condition sur la dimension de l'espace ambiant est discutée à travers le calcul, sous des hypothèse de régularité faibles pour le mécanisme de branchement, de la dimension de packing du range total du processus
This thesis investigates some fractal and pathwise properties of branching processes with continuous time and state-space. Informally, this kind of process can be described by considering the evolution of a population where individuals reproduce and die over time, randomly. The first chapter deals with the class of continuous branching processes with immigration. We provide a semi-explicit formula for the hitting times and a necessary and sufficient condition for the process to be recurrent or transient. Those two results illustrate the competition between branching and immigration. The second chapter deals with the Brownian tree and its local time measures : the level-sets measures. We show that they can be obtained as the restriction, with an explicit multiplicative constant, of a Hausdorff measure on the tree. The result holds uniformly for all levels. The third chapter study the Super-Brownian motion associated with a general branching mechanism. Its total occupation measure is obtained as the restriction to the total range, of a given packing measure on the euclidean space. The result is valid for large dimensions. The condition on the dimension is discussed by computing the packing dimension of the total range. This is done under a weak assumption on the regularity of the branching mechanism

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48

Afonso, Maria de Lourdes Belchior. "Evaluation of ruin probabilities for surplus processes with credibility and surplus dependent premiums." Doctoral thesis, Instituto Superior de Economia e Gestão, 2008. http://hdl.handle.net/10400.5/1113.

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Doutoramento em Matemática Aplicada à Economia e Gestão
In this dissertation we present a method for the numerical evaluation of the ruin prob¬ability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simu¬lation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming first a Brownian motion approximation and, secondly, a translated gamma distribution approximation for aggregate claim amounts. We will check the accuracy of our method by comparing our results applied to the classical risk process with the results of Wikstad (1971) and Seal (1978b) in finite and continuous time. We also check its accuracy in the case of exponential and mixed expo¬nential claim amounts by choosing a very long time horizon and comparing results with exact results for infinite time ruin. We apply our method to three different risk models where the premium is set at the start of each year but can change from year to year. For each model aggregate claims have a compound Poisson distribution with either a fixed or a variable Poisson parameter for the claim number process. For the first model the premium in each year is a function of the surplus level at the start of that, or an earlier, year. The premium rate is set so that the probability of ultimate ruin from that time is approximately equal to a pre-determined value. We will use De Vylder's (1978) approximation to achieve that. For the second and third models we consider a portfolio of risks which satisfy the assumptions of the Btihlmann or Btihlmann-Straub credibility models with the pure premium updated each year in accordance with these models.
E proposto um método para o cálculo da probabilidade de ruina em tempo contínuo e horizonte finito para um processo de Poisson composto onde o premio e constante ao longo de cada período de tempo (ano), mas depende da informação passada de indemnizacoes agregadas anuais. Em funçao disso, o premio e ajustado anualmente, passando a ser variavel de período para período. Um dos grandes contributos deste trabalho e o facto da metodologia apresentada ser facilmente aplicavel a carteiras de grande dimensao. O metodo e baseado na simulacão das indemnizacoes agregadas anuais e no calculo da probabilidade de ruína dado um determi¬nado montante de reserva no início e no fim do período. Este calculo da probabilidade de ruína e aproximado de duas formas: primeiro usando um movimento Browniano adequado e depois uma aproximaçao a distribuído gama deslocada. A coerencia dos resultados produzidos pelo modelo e testada comparando os resultados produzidos para o modelo clíassico de risco com o modelo-base e com os resultados exactos obtidos por Wikstad (1971) e por Seal (1978), em tempo contínuo e horizonte finito. O metodo e aplicado a tres modelos de risco diferentes em que o premio e actualizado no ínicio do ano. Para cada modelo as indemnizaçcãoes agregadas seguem uma distribuiçcãao de Poisson composta em que processo do nímero de sinistros tem o parâmetro de Poisson fixo ou variavel. No primeiro modelo o premio e definido como função do nível de reserva em algum momento anterior. O coeficiente de carga para o premio anual e determinado em cada caso de forma a probabilidade em horizonte infinito, partindo da reserva incial considerada, ser aproximadamente um valor pré-definido para o modelo classico. Para tal, e utilizada a aproximacão de De Vylder (1978). No segundo e terceiro modelos considera-se uma carteira que satisfaz as hipóteses dos modelos de credibilidade de Bühlmann e Bühlmann-Straub sendo o premio anual actualizado de acordo com estes modelos.

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49

Pereira, Gonçalo André Nunes. "Modelling sovereign debt with Lévy Processes." Master's thesis, Instituto Superior de Economia e Gestão, 2014. http://hdl.handle.net/10400.5/7611.

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Mestrado em Ciências Actuariais
Propomos modelizar o risco de crédito soberano de cinco países da zona Euro (Portugal, Irlanda, Itália, Grécia e Espanha) seguindo uma abordagem estrutural de primeira passagem em que o movimento Browniano geométrico é substituído por um processo de Lévy regido apenas por uma componente de saltos. Deste modo, introduzimos incrementos assimétricos e leptocúrticos e a possibilidade de incumprimento instantâneo, removendo assim algumas das principais limitações do modelo Black-Scholes. Calculamos a probabilidade de sobrevivência como preço de uma opção barreira discreta, utilizando um método de valorização de opções baseado na aproximação da densidade de transição como expansão em série de Fourier de cossenos. Assumindo uma taxa de recuperação determinística, calibramos o modelo de Lévy Carr-Geman-Madan-Yor (CGMY) utilizando spreads de Credit Default Swaps semanais e obtemos a estrutura temporal de probabilidades de incumprimento. Tiramos ainda partido da representação do processo Variance Gamma (uma instância do modelo CGMY) como movimento Browniano modificado temporalmente para considerar uma estrutura de dependência entre os riscos de crédito soberanos através de uma modificação temporal comum. Em seguida, ilustramos um possível procedimento de calibração multidimensional e obtemos a distribuição de sobrevivência conjunta via simulação.
We propose to model the sovereign credit risk of five Euro area countries (Portugal, Ireland, Italy, Greece and Spain) under a first passage structural approach, replacing the classical geometric Brownian motion dynamics with a pure jump Lévy process. This framework caters for skewness, fat tails and instantaneous defaults, thus addressing some of the main drawbacks of the Black-Scholes model. We compute the survival probability as the price of a discrete barrier option, using an option pricing method based on the approximation of the transition density as a Fourier-cosine series expansion. Assuming a deterministic recovery rate, we calibrate the Carr-Geman-Madan-Yor (CGMY) Lévy model to weekly Credit Default Swaps data and obtain the default probability term structure. By drawing on the representation of the Variance Gamma process (a particular instance of the CGMY model) as a time-changed Brownian motion, we accommodate dependency between sovereigns via a common time change. We then illustrate a possible multivariate calibration procedure and simulate the joint default distribution.

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50

Triampo, Wannapong. "Non-Equilibrium Disordering Processes In binary Systems Due to an Active Agent." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/26738.

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In this thesis, we study the kinetic disordering of systems interacting with an agent or a walker. Our studies divide naturally into two classes: for the first, the dynamics of the walker conserves the total magnetization of the system, for the second, it does not. These distinct dynamics are investigated in part I and II respectively. In part I, we investigate the disordering of an initially phase-segregated binary alloy due to a highly mobile vacancy which exchanges with the alloy atoms. This dynamics clearly conserves the total magnetization. We distinguish three versions of dynamic rules for the vacancy motion, namely a pure random walk , an ``active' and a biased walk. For the random walk case, we review and reproduce earlier work by Z. Toroczkai et. al.,~cite{TKSZ} which will serve as our base-line. To test the robustness of these findings and to make our model more accessible to experimental studies, we investigated the effects of finite temperatures (``active walks') as well as external fields (biased walks). To monitor the disordering process, we define a suitable disorder parameter, namely the number of broken bonds, which we study as a function of time, system size and vacancy number. Using Monte Carlo simulations and a coarse-grained field theory, we observe that the disordering process exhibits three well separated temporal regimes. We show that the later stages exhibit dynamic scaling, characterized by a set of exponents and scaling functions. For the random and the biased case, these exponents and scaling functions are computed analytically in excellent agreement with the simulation results. The exponents are remarkably universal. We conclude this part with some comments on the early stage, the interfacial roughness and other related features. In part II, we introduce a model of binary data corruption induced by a Brownian agent or random walker. Here, the magnetization is not conserved, being related to the density of corrupted bits }$ ho ${small .} {small Using both continuum theory and computer simulations, we study the average density of corrupted bits, and the associated density-density correlation function, as well as several other related quantities. In the second half, we extend our investigations in three main directions which allow us to make closer contact with real binary systems. These are i) a detailed analysis of two dimensions, ii) the case of competing agents, and iii) the cases of asymmetric and quenched random couplings. Our analytic results are in good agreement with simulation results. The remarkable finding of this study is the robustness of the phenomenological model which provides us with the tool, continuum theory, to understand the nature of such a simple model.
Ph. D.

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