Lévy Processes and Stochastic Calculus

Author: David Applebaum

Publisher: Cambridge University Press

ISBN: 9780521832632

Category: Mathematics

Page: 384

View: 6187

Graduate text decsribing two of the main tools for modern mathematical finance.

Lévy Processes and Infinitely Divisible Distributions

Author: Ken-iti Sato,Sato Ken-Iti

Publisher: Cambridge University Press

ISBN: 9780521553025

Category: Mathematics

Page: 486

View: 7422

This book provides the reader with comprehensive basic knowledge of Lévy processes.

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: 3816

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

Seminar on Stochastic Analysis, Random Fields and Applications V

Centro Stefano Franscini, Ascona, May 2005

Author: Robert Dalang,Marco Dozzi,Francesco Russo

Publisher: Springer Science & Business Media

ISBN: 9783764384586

Category: Mathematics

Page: 519

View: 9260

This volume contains refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 29 to June 3, 2004. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering.

Malliavin Calculus for Lévy Processes with Applications to Finance

Author: Giulia Di Nunno,Bernt Øksendal,Frank Proske

Publisher: Springer Science & Business Media

ISBN: 9783540785729

Category: Mathematics

Page: 418

View: 4886

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.

Stochastic Integration in Banach Spaces

Theory and Applications

Author: Vidyadhar Mandrekar,Barbara Rüdiger

Publisher: Springer

ISBN: 3319128531

Category: Mathematics

Page: 211

View: 6590

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​

Heavy-Tail Phenomena

Probabilistic and Statistical Modeling

Author: Sidney I. Resnick

Publisher: Springer Science & Business Media

ISBN: 0387242724

Category: Business & Economics

Page: 404

View: 3586

This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server and transmission rates of files are all examples of heavy-tailed phenomena. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus.

Stochastic Integrals

An Introduction

Author: Heinrich von Weizsäcker

Publisher: Springer-Verlag

ISBN: 3663139239

Category: Mathematics

Page: 332

View: 9581

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4746

Stochastic Processes

Author: Richard F. Bass

Publisher: Cambridge University Press

ISBN: 113950147X

Category: Mathematics

Page: N.A

View: 7133

This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Geometric Analysis

Author: Peter Li

Publisher: Cambridge University Press

ISBN: 1107020646

Category: Mathematics

Page: 406

View: 6955

Basic techniques for researchers interested in the field of geometric analysis.

Random Fragmentation and Coagulation Processes

Author: Jean Bertoin

Publisher: Cambridge University Press

ISBN: 1139459155

Category: Mathematics

Page: N.A

View: 8249

Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.

Introduction to Malliavin Calculus

Author: David Nualart,Eulalia Nualart

Publisher: Cambridge University Press

ISBN: 1107039126

Category: Business & Economics

Page: 246

View: 9861

This textbook offers a compact introductory course on Malliavin calculus, an active and powerful area of research. It covers recent applications, including density formulas, regularity of probability laws, central and non-central limit theorems for Gaussian functionals, convergence of densities and non-central limit theorems for the local time of Brownian motion. The book also includes a self-contained presentation of Brownian motion and stochastic calculus, as well as Lvy processes and stochastic calculus for jump processes. Accessible to non-experts, the book can be used by graduate students and researchers to develop their mastery of the core techniques necessary for further study.

Stochastic Calculus and Applications

Author: Samuel N. Cohen,Robert J. Elliott

Publisher: Birkhäuser

ISBN: 1493928678

Category: Mathematics

Page: 666

View: 7209

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 7703

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Stochastic Processes for Physicists

Understanding Noisy Systems

Author: Kurt Jacobs

Publisher: Cambridge University Press

ISBN: 1139486799

Category: Science

Page: 204

View: 2318

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.

A Course in Financial Calculus

Author: Alison Etheridge,Martin Baxter

Publisher: Cambridge University Press

ISBN: 9780521890779

Category: Business & Economics

Page: 196

View: 8299

A text for first courses in financial calculus; lots of examples and exercises, first published in 2002.