Lévy Processes

Author: Jean Bertoin

Publisher: Cambridge University Press

ISBN: 9780521646321

Category: Mathematics

Page: 266

View: 2395

This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.
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Lévy Processes

Theory and Applications

Author: Ole E. Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick

Publisher: Springer Science & Business Media

ISBN: 1461201977

Category: Mathematics

Page: 418

View: 3701

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.
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Lévy Processes in Lie Groups

Author: Ming Liao

Publisher: Cambridge University Press

ISBN: 9780521836531

Category: Mathematics

Page: 266

View: 8000

Up-to-the minute research on important stochastic processes.
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Exotic Option Pricing and Advanced Lévy Models

Author: Andreas Kyprianou,Wim Schoutens,Paul Wilmott

Publisher: John Wiley & Sons

ISBN: 0470017201

Category: Business & Economics

Page: 344

View: 783

Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
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XII Symposium of Probability and Stochastic Processes

Merida, Mexico, November 16–20, 2015

Author: Daniel Hernández-Hernández,Juan Carlos Pardo,Victor Rivero

Publisher: Springer

ISBN: 3319776436

Category: Mathematics

Page: 234

View: 7275

This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16–20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Bénédicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.
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Probability on Real Lie Algebras

Author: Uwe Franz,Nicolas Privault

Publisher: Cambridge University Press

ISBN: 110712865X

Category: Mathematics

Page: 302

View: 2933

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
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Lévy Processes

Author: Jean Bertoin

Publisher: Cambridge University Press

ISBN: 9780521562430

Category: Mathematics

Page: 275

View: 1477

This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.
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Convexity

Author: H. G. Eggleston

Publisher: CUP Archive

ISBN: 9780521077347

Category: Mathematics

Page: 141

View: 7932

This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.
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In Memoriam Paul-André Meyer - Séminaire de Probabilités XXXIX

Author: Marc Yor,Michel Émery

Publisher: Springer

ISBN: 9783540309949

Category: Mathematics

Page: 422

View: 593

The 39th volume of Séminaire de Probabilités is a tribute to the memory of Paul André Meyer. His life and achievements are recalled in this book, and tributes are paid by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance and Brownian motion. These contributions provide an overview on the current trends of stochastic calculus.
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ASTIN Bulletin

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Insurance

Page: N.A

View: 4023

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Annales de l'I.H.P.

Probabilités et statistiques

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Probabilities

Page: N.A

View: 7801

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Unsolved Problems of Noise and Fluctuations

UPoN'99: Second International Conference, Adelaide, Australia 11-15 July 1999

Author: Derek Abbott,Laszlo B. Kish

Publisher: American Inst. of Physics

ISBN: 9781563968266

Category: Mathematics

Page: 561

View: 329

Noise and fluctuations are at the seat of all physical systems. The advertised scope of the conference included gravitational wave detection, quantum fluctuations, quantum Brownian motion, Brownian ratchets, stochastic resonance, biological systems, semiconductors, electronic devices, sandpile physics, optical phenomena and all types of stochastic phenomena. This solicited a wide range of papers from cosmology to biology to electronic devices. Using the study of fluctuations as the unifying theme for these diverse disciplines is a new and exciting concept. UpoN is a unique conference in that it focuses on open questions and problems, rather than answers. 90% of the solution is asking the right question. The discovery of a problem is often more profound than the discovery of a solution. In the spirit of this conference, authors were asked to (1) conclude each manuscript with a section called "Conclusions and Open Questions" and (2) ask questions to the audience at the end of their oral presentation. An important characteristic of this conference is that refereeing of all papers was carried out to a high standard by the International Scientific Advisory Committee using a strict double-blind refereeing process.
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