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. 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.

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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), 202-208.- 2. On Some Exponential Functionals of Brownian Motion Adv. Appl. Prob. 24 (1992), 509-531.- 3. Some Relations between Bessel Processes, Asian Options and Confluent Hypergeometric Functions C.R. Acad. Sci., Paris, Sér. I 314 (1992), 417-474 (with Hélyette Geman).- 4. The Laws of Exponential Functionals of Brownian Motion, Taken at Various Random Times C.R. Acad. Sci., Paris, Sér. I 314 (1992), 951-956.- 5. Bessel Processes, Asian Options, and Perpetuities Mathematical Finance, Vol. 3, No. 4 (October 1993), 349-375 (with Hélyette Geman).- 6. Further Results on Exponential Functionals of Brownian Motion.- 7. From Planar Brownian Windings to Asian Options Insurance: Mathematics and Economics 13 (1993), 23-34.- 8. On Exponential Functionals of Certain Lévy Processes Stochastics and Stochastic Rep. 47 (1994), 71-101 (with P. Carmona and F. Petit).- 9. On Some Exponential-integral Functionals of Bessel Processes Mathematical Finance, Vol. 3 No. 2 (April 1993), 231-240.- 10. Exponential Functionals of Brownian Motion and Disordered Systems J. App. Prob. 35 (1998), 255-271 (with A. Comtet and C. Monthus).