Hiroyuki Matsumoto, Marc Yor
Published 2005-11-21, updated 2007-04-26Version 2
This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and extensions of L\'{e}vy's and Pitman's theorems are discussed.
Comments: Published at http://dx.doi.org/10.1214/154957805100000168 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Probability Surveys 2005, Vol. 2, 348-384
On Besov regularity of Brownian motions in infinite dimensions
Configurations of balls in Euclidean space that Brownian motion cannot avoid
Nonlinear boundary crossing probabilities of Brownian motion with random jumps
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