| Exponential Functionals of Brownian Motion and Related Processes Softcover Repri Edition Contributor(s): Yor, Marc (Author) |
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ISBN: 3540659439 ISBN-13: 9783540659433 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: August 2001 Annotation: This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between 1988 and 1998. These functionals play an important role in Mathematical Finance, as well as in (probabilistic) studies related to hyperbolic geometry, and also to random media. Throughout the volume, connections with more recent studies involving exponential functionals of L??vy processes are indicated. Some papers originally published in French are made available in English for the first time. |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Business & Economics | Finance - General - Mathematics | Probability & Statistics - General |
| Dewey: 519.233 |
| LCCN: 2001020860 |
| Physical Information: 0.46" H x 6.14" W x 9.21" (0.69 lbs) 206 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |