Applications Of Lévy Processes

Author : Oleg Kudryavtsev,Antonino Zanette
Publisher : Nova Science Publishers
Page : 259 pages
File Size : 48,6 Mb
Release : 2021
Category : Mathematics
ISBN : 1536198498

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Applications of Lévy Processes by Oleg Kudryavtsev,Antonino Zanette Pdf

"Lévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black-Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black-Scholes model, and regime-switching Lévy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorization. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book"--

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 50,9 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 : Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201977

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Lévy Processes by Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Author : Giulia Di Nunno,Bernt Øksendal,Frank Proske
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 52,7 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9783540785729

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Malliavin Calculus for Lévy Processes with Applications to Finance by Giulia Di Nunno,Bernt Øksendal,Frank Proske Pdf

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

Author : Ole E. Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Birkhauser
Page : 415 pages
File Size : 40,7 Mb
Release : 2001-01-01
Category : Lévy processes
ISBN : 376434167X

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Lévy Processes by Ole E. Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

Author : Björn Böttcher,René Schilling,Jian Wang
Publisher : Springer
Page : 199 pages
File Size : 51,9 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9783319026848

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Lévy Matters III by Björn Böttcher,René Schilling,Jian Wang Pdf

This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is a counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 41,5 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 : David Applebaum
Publisher : Cambridge University Press
Page : 461 pages
File Size : 55,6 Mb
Release : 2009-04-30
Category : Mathematics
ISBN : 9781139477987

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Lévy Processes and Stochastic Calculus by David Applebaum Pdf

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Author : Davar Khoshnevisan,René Schilling
Publisher : Birkhäuser
Page : 220 pages
File Size : 49,9 Mb
Release : 2016-12-22
Category : Mathematics
ISBN : 9783319341200

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From Lévy-Type Processes to Parabolic SPDEs by Davar Khoshnevisan,René Schilling Pdf

This volume presents the lecture notes from two courses given by Davar Khoshnevisan and René Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. René Schilling’s notes are an expanded version of his course on Lévy and Lévy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Lévy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lévy-Itô decomposition. On the other, it identifies the infinitesimal generator of the Lévy process as a pseudo-differential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lévy processes. The presentation is self-contained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan’s course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparison-type results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative space-time white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lévy process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples.

Author : Mohamed Abdel-Hameed
Publisher : Springer Science & Business Media
Page : 126 pages
File Size : 43,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783642400759

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Lévy Processes and Their Applications in Reliability and Storage by Mohamed Abdel-Hameed Pdf

​This book covers Lévy processes and their applications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degradation; estimating the parameters of the degradation process is also discussed, as is the maintenance of dams subject to Lévy input.

Author : Andreas E. Kyprianou,Juan Carlos Pardo
Publisher : Cambridge University Press
Page : 485 pages
File Size : 44,7 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 : Loïc Chaumont,Andreas E. Kyprianou
Publisher : Springer Nature
Page : 354 pages
File Size : 54,7 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 : Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero
Publisher : Springer
Page : 200 pages
File Size : 40,5 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9783642314070

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Lévy Matters II by Serge Cohen,Alexey Kuznetsov,Andreas E. Kyprianou,Victor Rivero Pdf

This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.

Author : Andreas E. Kyprianou
Publisher : Unknown
Page : 476 pages
File Size : 42,5 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 : Franziska Kühn
Publisher : Springer
Page : 245 pages
File Size : 46,6 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9783319608884

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Lévy Matters VI by Franziska Kühn Pdf

Presenting some recent results on the construction and the moments of Lévy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Lévy-type processes to existence and uniqueness theorems for Lévy-driven stochastic differential equations with Hölder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Lévy-type processes are studied and some estimates on moments are derived. Lévy-type processes behave locally like Lévy processes but, in contrast to Lévy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Lévy-driven stochastic differential equations. This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.