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Exponential Functionals of Brownian Motion and Related Processes
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 Lévy processes are indicated. Some papers originally published in French are made available in English for the first time.
On certain exponential functions of real Brownian motion -- On Some Exponential Functionals of Brownian Motion -- Some relations between Bessel processes, Asian options and confluent hypergeometric functions -- The laws of exponential functions of Brownian motion, taken at various random times -- Bessel Processes, Asian option and perpetuities -- Further Results on Exponential Functionals of Brownian Motion -- From Planar Brownian Windings to Asian Options -- On exponential functions of certain Lévy processes -- On Some Exponential-Integral Functionals of Bessel Processes -- Exponential Functionals of Brownian Motion and Disordered Systems.