CHANGE OF TIME AND CHANGE OF MEASURE (SECOND EDITION) (Advanced Statistical Science and Applied Probability)

Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.

Reviews of the First Edition:

"This book is a beautiful and well-articulated monograph, full of information, where the interplay between deep mathematical ideas and extremely explicit applied financial problems and their solutions is generously exemplified. The style of presentation and the contents makes this enjoyable book ideal for a reader interested in going deeper in understanding the area or in having a panoramic view of it. For that category of readers, this book will certainly provide an opportunity to learn additional results and to establish beautiful connections between them, all of it elegantly illustrated with one of the most relevant and impressive applications of this mathematical field." -- EMS Newsletter

"The interested reader will find in this book a useful introduction to stochastic calculus for continuous and jump processes as well as a much needed single reference source for the relevant connections between change of time, stochastic integral representation, and the Girsanov theorem." -- Mathematical Reviews