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Levy Processes In Finance


Levy Processes In Finance
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L Vy Processes


L Vy Processes
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Author : Ole E Barndorff-Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

L Vy Processes written by Ole E Barndorff-Nielsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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.



Fluctuations Of L Vy Processes With Applications


Fluctuations Of L Vy Processes With Applications
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Author : Andreas E. Kyprianou
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-09

Fluctuations Of L Vy Processes With Applications written by Andreas E. Kyprianou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.


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.



Financial Modelling With Jump Processes


Financial Modelling With Jump Processes
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Author : Rama Cont
language : en
Publisher: CRC Press
Release Date : 2003-12-30

Financial Modelling With Jump Processes written by Rama Cont and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-30 with Business & Economics categories.


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



L Vy Processes And Stochastic Calculus


L Vy Processes And Stochastic Calculus
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-30

L Vy Processes And Stochastic Calculus written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-30 with Mathematics categories.


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.



Stochastic Processes


Stochastic Processes
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Author : Wolfgang Paul
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-11

Stochastic Processes written by Wolfgang Paul and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-11 with Science categories.


This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.



Cambridge Tracts In Mathematics


Cambridge Tracts In Mathematics
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Author : Jean Bertoin
language : en
Publisher: Cambridge University Press
Release Date : 1996

Cambridge Tracts In Mathematics written by Jean Bertoin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


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



Option Pricing In Incomplete Markets


Option Pricing In Incomplete Markets
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Author : Yoshio Miyahara
language : en
Publisher: World Scientific
Release Date : 2012

Option Pricing In Incomplete Markets written by Yoshio Miyahara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Electronic books categories.


This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem



Mathematical Finance


Mathematical Finance
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Author : Ernst Eberlein
language : en
Publisher: Springer Nature
Release Date : 2019-12-03

Mathematical Finance written by Ernst Eberlein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-03 with Mathematics categories.


Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.



Mathematical Methods For Financial Markets


Mathematical Methods For Financial Markets
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Author : Monique Jeanblanc
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03

Mathematical Methods For Financial Markets written by Monique Jeanblanc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-03 with Business & Economics categories.


Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.



Levy Processes In Finance


Levy Processes In Finance
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Author : Wim Schoutens
language : en
Publisher: Wiley
Release Date : 2003-05-07

Levy Processes In Finance written by Wim Schoutens and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-07 with Mathematics categories.


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.