Stochastic Calculus of Variations in Mathematical Finance

Stochastic Calculus of Variations in Mathematical Finance
Author :
Publisher : Springer Science & Business Media
Total Pages : 148
Release :
ISBN-10 : 9783540307990
ISBN-13 : 3540307990
Rating : 4/5 (90 Downloads)

Synopsis Stochastic Calculus of Variations in Mathematical Finance by : Paul Malliavin

Highly esteemed author Topics covered are relevant and timely

Stochastic Calculus of Variations

Stochastic Calculus of Variations
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 362
Release :
ISBN-10 : 9783110392326
ISBN-13 : 3110392321
Rating : 4/5 (26 Downloads)

Synopsis Stochastic Calculus of Variations by : Yasushi Ishikawa

This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index

Analysis of Variations for Self-similar Processes

Analysis of Variations for Self-similar Processes
Author :
Publisher : Springer Science & Business Media
Total Pages : 272
Release :
ISBN-10 : 9783319009360
ISBN-13 : 3319009362
Rating : 4/5 (60 Downloads)

Synopsis Analysis of Variations for Self-similar Processes by : Ciprian Tudor

Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.

Malliavin Calculus and Stochastic Analysis

Malliavin Calculus and Stochastic Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 580
Release :
ISBN-10 : 9781461459064
ISBN-13 : 1461459060
Rating : 4/5 (64 Downloads)

Synopsis Malliavin Calculus and Stochastic Analysis by : Frederi Viens

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitful interpretation of this calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers, presented their cutting-edge research at an international conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume.

A Modern Theory of Random Variation

A Modern Theory of Random Variation
Author :
Publisher : John Wiley & Sons
Total Pages : 493
Release :
ISBN-10 : 9781118345948
ISBN-13 : 1118345940
Rating : 4/5 (48 Downloads)

Synopsis A Modern Theory of Random Variation by : Patrick Muldowney

A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

Stochastic Analysis for Poisson Point Processes

Stochastic Analysis for Poisson Point Processes
Author :
Publisher : Springer
Total Pages : 359
Release :
ISBN-10 : 9783319052335
ISBN-13 : 3319052330
Rating : 4/5 (35 Downloads)

Synopsis Stochastic Analysis for Poisson Point Processes by : Giovanni Peccati

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

Lévy Processes and Stochastic Calculus

Lévy Processes and Stochastic Calculus
Author :
Publisher : Cambridge University Press
Total Pages : 461
Release :
ISBN-10 : 9781139477987
ISBN-13 : 1139477986
Rating : 4/5 (87 Downloads)

Synopsis Lévy Processes and Stochastic Calculus by : David Applebaum

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.

Introduction to Stochastic Calculus with Applications

Introduction to Stochastic Calculus with Applications
Author :
Publisher : Imperial College Press
Total Pages : 431
Release :
ISBN-10 : 9781860945557
ISBN-13 : 1860945554
Rating : 4/5 (57 Downloads)

Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Applied Stochastic Differential Equations

Applied Stochastic Differential Equations
Author :
Publisher : Cambridge University Press
Total Pages : 327
Release :
ISBN-10 : 9781316510087
ISBN-13 : 1316510085
Rating : 4/5 (87 Downloads)

Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

The Malliavin Calculus

The Malliavin Calculus
Author :
Publisher : Courier Corporation
Total Pages : 124
Release :
ISBN-10 : 9780486152059
ISBN-13 : 0486152057
Rating : 4/5 (59 Downloads)

Synopsis The Malliavin Calculus by : Denis R. Bell

This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.