Levy Processes

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Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3642376320
Total Pages : 461 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou

Download or read book Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461201977
Total Pages : 414 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lévy Processes by : Ole E Barndorff-Nielsen

Download or read book Lévy Processes written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes and Stochastic Calculus

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 1139477986
Total Pages : 461 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2009-04-30 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Levy Processes in Finance

Author : Wim Schoutens
Publisher : Wiley
ISBN 13 : 9780470851562
Total Pages : 200 pages
Book Rating : 4.8/5 (515 download)

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Book Synopsis Levy Processes in Finance by : Wim Schoutens

Download or read book Levy Processes in Finance written by Wim Schoutens and published by Wiley. This book was released on 2003-05-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of L?vy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. L?vy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of L?vy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of L?vy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers.

Malliavin Calculus for Lévy Processes with Applications to Finance

Author : Giulia Di Nunno
Publisher : Springer Science & Business Media
ISBN 13 : 3540785728
Total Pages : 421 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Malliavin Calculus for Lévy Processes with Applications to Finance by : Giulia Di Nunno

Download or read book Malliavin Calculus for Lévy Processes with Applications to Finance written by Giulia Di Nunno and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes in Lie Groups

Author : Ming Liao
Publisher : Cambridge University Press
ISBN 13 : 9780521836531
Total Pages : 292 pages
Book Rating : 4.8/5 (365 download)

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Book Synopsis Lévy Processes in Lie Groups by : Ming Liao

Download or read book Lévy Processes in Lie Groups written by Ming Liao and published by Cambridge University Press. This book was released on 2004-05-10 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Up-to-the minute research on important stochastic processes.

Lévy Processes and Infinitely Divisible Distributions

Author : Sato Ken-Iti
Publisher : Cambridge University Press
ISBN 13 : 9780521553025
Total Pages : 504 pages
Book Rating : 4.5/5 (53 download)

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Book Synopsis Lévy Processes and Infinitely Divisible Distributions by : Sato Ken-Iti

Download or read book Lévy Processes and Infinitely Divisible Distributions written by Sato Ken-Iti and published by Cambridge University Press. This book was released on 1999 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lévy Matters III

Author : Björn Böttcher
Publisher : Springer
ISBN 13 : 3319026844
Total Pages : 215 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Lévy Matters III by : Björn Böttcher

Download or read book Lévy Matters III written by Björn Böttcher and published by Springer. This book was released on 2014-01-16 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introductory Lectures on Fluctuations of Lévy Processes with Applications

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
ISBN 13 : 3540313435
Total Pages : 382 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Introductory Lectures on Fluctuations of Lévy Processes with Applications by : Andreas E. Kyprianou

Download or read book Introductory Lectures on Fluctuations of Lévy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2006-12-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cambridge Tracts in Mathematics

Author : Jean Bertoin
Publisher : Cambridge University Press
ISBN 13 : 9780521646321
Total Pages : 292 pages
Book Rating : 4.6/5 (463 download)

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Book Synopsis Cambridge Tracts in Mathematics by : Jean Bertoin

Download or read book Cambridge Tracts in Mathematics written by Jean Bertoin and published by Cambridge University Press. This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

Financial Models with Levy Processes and Volatility Clustering

Author : Svetlozar T. Rachev
Publisher : John Wiley & Sons
ISBN 13 : 0470937262
Total Pages : 316 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Financial Models with Levy Processes and Volatility Clustering by : Svetlozar T. Rachev

Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Lévy Processes and Infinitely Divisible Distributions

Author : 健一·佐藤
Publisher :
ISBN 13 : 9780521553025
Total Pages : 486 pages
Book Rating : 4.5/5 (53 download)

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Book Synopsis Lévy Processes and Infinitely Divisible Distributions by : 健一·佐藤

Download or read book Lévy Processes and Infinitely Divisible Distributions written by 健一·佐藤 and published by . This book was released on 1999-11-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.

From Lévy-Type Processes to Parabolic SPDEs

Author : Davar Khoshnevisan
Publisher : Birkhäuser
ISBN 13 : 3319341200
Total Pages : 214 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis From Lévy-Type Processes to Parabolic SPDEs by : Davar Khoshnevisan

Download or read book From Lévy-Type Processes to Parabolic SPDEs written by Davar Khoshnevisan and published by Birkhäuser. This book was released on 2016-12-22 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes and Stochastic Calculus

Author : David Applebaum
Publisher : Cambridge University Press
ISBN 13 : 9780521832632
Total Pages : 440 pages
Book Rating : 4.8/5 (326 download)

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Book Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

Download or read book Lévy Processes and Stochastic Calculus written by David Applebaum and published by Cambridge University Press. This book was released on 2004-07-05 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Financial Modelling with Jump Processes

Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Financial Modelling with Jump Processes by : Peter Tankov

Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Levy Processes in Credit Risk

Author : Wim Schoutens
Publisher : John Wiley & Sons
ISBN 13 : 0470685069
Total Pages : 213 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis Levy Processes in Credit Risk by : Wim Schoutens

Download or read book Levy Processes in Credit Risk written by Wim Schoutens and published by John Wiley & Sons. This book was released on 2010-06-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory guide to using Lévy processes for credit risk modelling. It covers all types of credit derivatives: from the single name vanillas such as Credit Default Swaps (CDSs) right through to structured credit risk products such as Collateralized Debt Obligations (CDOs), Constant Proportion Portfolio Insurances (CPPIs) and Constant Proportion Debt Obligations (CPDOs) as well as new advanced rating models for Asset Backed Securities (ABSs). Jumps and extreme events are crucial stylized features, essential in the modelling of the very volatile credit markets - the recent turmoil in the credit markets has once again illustrated the need for more refined models. Readers will learn how the classical models (driven by Brownian motions and Black-Scholes settings) can be significantly improved by using the more flexible class of Lévy processes. By doing this, extreme event and jumps can be introduced into the models to give more reliable pricing and a better assessment of the risks. The book brings in high-tech financial engineering models for the detailed modelling of credit risk instruments, setting up the theoretical framework behind the application of Lévy Processes to Credit Risk Modelling before moving on to the practical implementation. Complex credit derivatives structures such as CDOs, ABSs, CPPIs, CPDOs are analysed and illustrated with market data.

Stochastic Processes for Physicists

Author : Kurt Jacobs
Publisher : Cambridge University Press
ISBN 13 : 1139486799
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Stochastic Processes for Physicists by : Kurt Jacobs

Download or read book Stochastic Processes for Physicists written by Kurt Jacobs and published by Cambridge University Press. This book was released on 2010-02-18 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.