Exponential Functionals of Brownian Motion and Related Processes

Language: English

Published by J.B. Metzler, 2001

3540659439 / 9783540659433

Series: Book 5 of 53 - Springer Finance

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Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | This monograph contains: - ten papers written by the author, and co-authors, between December 1988 and October 1998 about certain exponential functionals of Brownian motion and related processes, which have been, and still are, of interest, during at least the last decade, to researchers in Mathematical finance; - an introduction to the subject from the view point of Mathematical Finance by H. Geman. The origin of my interest in the study of exponentials of Brownian motion in relation with mathematical finance is the question, first asked to me by S. Jacka in Warwick in December 1988, and later by M. Chesney in Geneva, and H. Geman in Paris, to compute the price of Asian options, i. e. : to give, as much as possible, an explicit expression for: (1) where A~v) = I~ dsexp2(Bs + liS), with (Bs,s::::: 0) a real-valued Brownian motion. Since the exponential process of Brownian motion with drift, usually called: geometric Brownian motion, may be represented as: t ::::: 0, (2) where (Rt), u ::::: 0) denotes a 15-dimensional Bessel process, with 5 = 2(1I+1), it seemed clear that, starting from (2) [which is analogous to Feller's repre­ sentation of a linear diffusion X in terms of Brownian motion, via the scale function and the speed measure of X], it should be possible to compute quan­ tities related to (1), in particular: in hinging on former computations for Bessel processes.

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Title
Exponential Functionals of Brownian Motion and Related Processes
Author
Yor, Marc
Publisher
J.B. Metzler
Publication year
2001
Condition
Sehr gut
Binding
Soft cover
Language
English
ISBN 10
3540659439
ISBN 13
9783540659433
Series
Book 5 of 53: Springer Finance
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Buchpark

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