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On Exponential Functionals of Brownian Motion and Related Processes

Marc Yor

This book is a collection of papers that deal with the laws of Geometric Brownian Motion and their time-integrals with an emphasis on Asian Options. Each paper is self-contained and presents the topics at a high level. Therefore, this book requires some previous knowledge of the subject. However, it's clear style makes it more accessible then one would first anticipate provided that the reader has a good mathematical background and knowledge in probability theory. Much of the papers deal with topics in which there is a great deal of recent research being carried out. Thus, this book provides a valuable reference for people investigating and applying this mathematics to the study of Asian Options. The author begins with a short introductory chapter on functionals of Brownian Motion in Finance and gives a good account to the problems involved. The following chapters are a collection of papers written by the author and co-authors between 1988 and 1998. A list of these are:

On certain exponential functions of real Brownian Motion.
On some exponential functionals of Brownian Motion.
Some relations between Bessel Processes, Asian options and confluent hypergeomertric functions.
The laws of exponential functions of Brownian Motion, taken at various random times. Bessel processes, Asian option and perpetuities.
Further results on exponential Functionals of Brownian Motion.
From planar Brownian Widings to Asian options.
On Exponential Functions of certain Levy processes.
On some exponential-integral functionals of Bessel Processes.
Exponential functionals of Brownian Motion and Disordered Systems.

Reviewed by Moreno Fasolo. Click here to buy this book at Amazon.co.uk.

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