Author	Yor, Marc. author
Title	Exponential Functionals of Brownian Motion and Related Processes [electronic resource] / by Marc Yor
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
Connect to	http://dx.doi.org/10.1007/978-3-642-56634-9
Descript	X, 206 p. online resource

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 Aṽ) = Ĩ 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 repreยญ 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 quanยญ tities related to (1), in particular: in hinging on former computations for Bessel processes

0. Functionals of Brownian Motion in Finance and in Insurance -- 1. On Certain Exponential Functionals of Real-Valued Brownian Motion J Appl. Prob. 29 (1992), 202โ208 -- 2. On Some Exponential Functionals of Brownian Motion Adv. Appl. Prob. 24 (1992), 509โ531 -- 3. Some Relations between Bessel Processes, Asian Options and Confluent Hypergeometric Functions C.R. Acad. Sci., Paris, Sรฉr. I 314 (1992), 417โ474 (with Hรฉlyette Geman) -- 4. The Laws of Exponential Functionals of Brownian Motion, Taken at Various Random Times C.R. Acad. Sci., Paris, Sรฉr. I 314 (1992), 951โ956 -- 5. Bessel Processes, Asian Options, and Perpetuities Mathematical Finance, Vol. 3, No. 4 (October 1993), 349โ375 (with Hรฉlyette Geman) -- 6. Further Results on Exponential Functionals of Brownian Motion -- 7. From Planar Brownian Windings to Asian Options Insurance: Mathematics and Economics 13 (1993), 23โ34 -- 8. On Exponential Functionals of Certain Lรฉvy Processes Stochastics and Stochastic Rep. 47 (1994), 71โ101 (with P. Carmona and F. Petit) -- 9. On Some Exponential-integral Functionals of Bessel Processes Mathematical Finance, Vol. 3 No. 2 (April 1993), 231โ240 -- 10. Exponential Functionals of Brownian Motion and Disordered Systems J. App. Prob. 35 (1998), 255โ271 (with A. Comtet and C. Monthus)

1. Mathematics
2. Economics
3. Mathematical
4. Probabilities
5. Mathematics
6. Probability Theory and Stochastic Processes
7. Quantitative Finance