A Martingale Review of Some Fluctuation Theory for Spectrally Negative Lévy Processes
Author: Andreas E. Kyprianou
Publisher:
Published: 2003
Total Pages: 11
ISBN-13:
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Author: Andreas E. Kyprianou
Publisher:
Published: 2003
Total Pages: 11
ISBN-13:
DOWNLOAD EBOOKAuthor: Ronald A. Doney
Publisher: Springer
Published: 2007-04-25
Total Pages: 154
ISBN-13: 3540485112
DOWNLOAD EBOOKLévy 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: Andreas E. Kyprianou
Publisher: Springer Science & Business Media
Published: 2014-01-09
Total Pages: 461
ISBN-13: 3642376320
DOWNLOAD EBOOKLévy 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: Michel Émery
Publisher: Springer
Published: 2004-11-15
Total Pages: 402
ISBN-13: 3540314490
DOWNLOAD EBOOKBesides a series of six articles on Lévy processes, Volume 38 of the Séminaire de Probabilités contains contributions whose topics range from analysis of semi-groups to free probability, via martingale theory, Wiener space and Brownian motion, Gaussian processes and matrices, diffusions and their applications to PDEs. As do all previous volumes of this series, it provides an overview on the current state of the art in the research on stochastic processes.
Author: Catherine Donati-Martin
Publisher: Springer Science & Business Media
Published: 2008-05-07
Total Pages: 459
ISBN-13: 3540779124
DOWNLOAD EBOOKStochastic processes are as usual the main subject of the Séminaire, with contributions on Brownian motion (fractional or other), Lévy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.
Author: Erik Jan Baurdoux
Publisher:
Published: 2007
Total Pages: 129
ISBN-13: 9789039346211
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 2008
Total Pages: 484
ISBN-13:
DOWNLOAD EBOOKContents of 1-14 (1966/67-1978/79) in v. 15 (1979/80)
Author: Serge Cohen
Publisher: Springer
Published: 2012-09-14
Total Pages: 200
ISBN-13: 3642314074
DOWNLOAD EBOOKThis 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: Peter Tankov
Publisher: CRC Press
Published: 2003-12-30
Total Pages: 552
ISBN-13: 1135437947
DOWNLOAD EBOOKWINNER 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