Overview
It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on ""unusual"" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.
Full Product Details
Author: Mohamed Abdelghani ,
Alexander Melnikov
Publisher: Taylor & Francis Ltd
Imprint: CRC Press
Weight: 0.843kg
ISBN: 9781138337268
ISBN 10: 1138337269
Pages: 392
Publication Date: 14 July 2020
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
Modern stochastics is usually identified with stochastic analysis, a field in mathematics that is well-developed under usual conditions . Hence, a variety of results of this theory and its applications are also restricted by these technical conditions. Many examples from theory and applications call for further extensions of stochastic analysis. Optional Processes: Theory and Applications is first attempt of such natural extension. The authors provide an excellent treatment of papers written in the 1970s and 1980s by Dellacherie, Doob, Galtchouk, Lepingle, and Lenglart among others. Moreover, the authors develop this topic in a comprehensive manner, and while doing so offer beautiful applications to the fields of mathematical finance and filtering theory. This book will be extremely useful for experts in the area of stochastic analysis, mathematical finance, and related fields. -Svetlozar Rachev, Texas Tech University
Author Information
Mohamed Abdelghani completed his PhD in Mathematical Finance from the University of Alberta. He is currently working as a V.P. in quantitative finance and machine learning at Morgan Stanley, New York, USA. Alexander Melnikov is a Professor in Mathematical Finance at the University of Alberta, Edmonton, Canada. His research interests belong to the area of contemporary stochastic analysis and its numerous applications in Mathematical Finance, Statistics and Actuarial Science. He has written six books as well as over one hundred research papers in leading academic journals.
