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Exponential Functionals of Brownian Motion and Related Processes

Exponential Functionals of Brownian Motion and Related Processes

Exponential Functionals of Brownian Motion and Related Processes Paperback - 2001

by Marc Yor

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Details

  • Title Exponential Functionals of Brownian Motion and Related Processes
  • Author Marc Yor
  • Binding Paperback
  • Edition Softcover reprin
  • Condition New
  • Pages 206
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Publication date 2001-08-14
  • Illustrated Yes
  • Features Illustrated
  • Bookseller's Inventory # ria9783540659433_inp
  • ISBN 9783540659433 / 3540659439
  • Weight 0.69 lbs (0.31 kg)
  • Dimensions 9.21 x 6.14 x 0.46 in (23.39 x 15.60 x 1.17 cm)
  • Category Mathematics
  • Library of Congress Catalogue Number 2001020860
  • Dewey Decimal Code 519.233
  • Quantity available 492

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From the publisher

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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