Fluctuations Of Lévy Processes With Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 49,5 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9783642376320

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Fluctuations of Lévy Processes with Applications by Andreas E. Kyprianou Pdf

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 44,6 Mb
Release : 2006-12-18
Category : Mathematics
ISBN : 9783540313434

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Introductory Lectures on Fluctuations of Lévy Processes with Applications by Andreas E. Kyprianou Pdf

This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.

Author : Andreas E. Kyprianou
Publisher : Unknown
Page : 476 pages
File Size : 50,8 Mb
Release : 2014-01-31
Category : Electronic
ISBN : 3642376339

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Fluctuations of Levy Processes with Applications by Andreas E. Kyprianou Pdf

Author : Ronald A. Doney
Publisher : École d'Été de Probabilités de Saint-Flour
Page : 168 pages
File Size : 55,8 Mb
Release : 2007-04-19
Category : Mathematics
ISBN : UVA:X030236690

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Fluctuation Theory for Lévy Processes by Ronald A. Doney Pdf

Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Author : Ronald A. Doney
Publisher : Springer
Page : 154 pages
File Size : 49,5 Mb
Release : 2007-04-25
Category : Mathematics
ISBN : 9783540485117

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Fluctuation Theory for Lévy Processes by Ronald A. Doney Pdf

Lévy processes, that is, processes in continuous time with stationary and independent increments, form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, and of course finance, where they include particularly important examples having "heavy tails." Their sample path behaviour poses a variety of challenging and fascinating problems, which are addressed in detail.

Author : Krzysztof Dębicki,Michel Mandjes
Publisher : Springer
Page : 255 pages
File Size : 48,7 Mb
Release : 2015-08-06
Category : Mathematics
ISBN : 9783319206936

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Queues and Lévy Fluctuation Theory by Krzysztof Dębicki,Michel Mandjes Pdf

The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.

Author : Andreas E. Kyprianou,Juan Carlos Pardo
Publisher : Cambridge University Press
Page : 485 pages
File Size : 53,6 Mb
Release : 2022-04-07
Category : Mathematics
ISBN : 9781108480291

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Stable Lévy Processes via Lamperti-Type Representations by Andreas E. Kyprianou,Juan Carlos Pardo Pdf

A systematic treatment of stable Lévy processes and self-similar Markov processes, for graduate students and researchers in the field.

Author : Robert Dalang,Marco Dozzi,Francesco Russo
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 40,9 Mb
Release : 2011-03-16
Category : Mathematics
ISBN : 9783034800211

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Seminar on Stochastic Analysis, Random Fields and Applications VI by Robert Dalang,Marco Dozzi,Francesco Russo Pdf

This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.

Author : Loïc Chaumont,Andreas E. Kyprianou
Publisher : Springer Nature
Page : 354 pages
File Size : 41,6 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030833091

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A Lifetime of Excursions Through Random Walks and Lévy Processes by Loïc Chaumont,Andreas E. Kyprianou Pdf

This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.

Author : Catherine Donati-Martin,Antoine Lejay,Alain Rouault
Publisher : Springer Nature
Page : 399 pages
File Size : 40,8 Mb
Release : 2022-05-13
Category : Mathematics
ISBN : 9783030964092

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Séminaire de Probabilités LI by Catherine Donati-Martin,Antoine Lejay,Alain Rouault Pdf

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs. The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

Author : Alfonso Rocha-Arteaga,Ken-iti Sato
Publisher : Springer Nature
Page : 135 pages
File Size : 40,6 Mb
Release : 2019-11-02
Category : Mathematics
ISBN : 9783030227005

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Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition by Alfonso Rocha-Arteaga,Ken-iti Sato Pdf

This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions Lm, m = 0,1,...,∞, from the class L0 of selfdecomposable distributions to the class L∞ generated by stable distributions through convolution and convergence. The book is divided into five chapters. Chapter 1 studies basic properties of Lm classes needed for the subsequent chapters. Chapter 2 introduces Ornstein-Uhlenbeck type processes generated by a Lévy process through stochastic integrals based on Lévy processes. Necessary and sufficient conditions are given for a generating Lévy process so that the OU type process has a limit distribution of Lm class. Chapter 3 establishes the correspondence between selfsimilar additive processes and selfdecomposable distributions and makes a close inspection of the Lamperti transformation, which transforms selfsimilar additive processes and stationary type OU processes to each other. Chapter 4 studies multivariate subordination of a cone-parameter Lévy process by a cone-valued Lévy process. Finally, Chapter 5 studies strictly stable and Lm properties inherited by the subordinated process in multivariate subordination. In this revised edition, new material is included on advances in these topics. It is rewritten as self-contained as possible. Theorems, lemmas, propositions, examples and remarks were reorganized; some were deleted and others were newly added. The historical notes at the end of each chapter were enlarged. This book is addressed to graduate students and researchers in probability and mathematical statistics who are interested in learning more on Lévy processes and infinitely divisible distributions.

Author : David Applebaum
Publisher : Cambridge University Press
Page : 491 pages
File Size : 49,8 Mb
Release : 2009-04-30
Category : Mathematics
ISBN : 9780521738651

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

A fully revised and appended edition of this unique volume, which develops together these two important subjects.

Author : Andrey Itkin
Publisher : Birkhäuser
Page : 308 pages
File Size : 44,7 Mb
Release : 2017-02-27
Category : Mathematics
ISBN : 9781493967926

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Pricing Derivatives Under Lévy Models by Andrey Itkin Pdf

This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

Author : Julia Di Nunno,Bernt Øksendal
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 40,8 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642184123

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Advanced Mathematical Methods for Finance by Julia Di Nunno,Bernt Øksendal Pdf

This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Author : Michel Mandjes,Onno Boxma
Publisher : Springer Nature
Page : 252 pages
File Size : 52,8 Mb
Release : 2023-12-29
Category : Mathematics
ISBN : 9783031391057

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The Cramér–Lundberg Model and Its Variants by Michel Mandjes,Onno Boxma Pdf

This book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants. Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér–Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology. This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.