Exponential functionals of Brownian motion, I: Probability laws at fixed time

Hiroyuki Matsumoto · Marc Yor

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

Abstract

This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.

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References

1999Continuous Martingales and Brownian Motion 1991Continuous Martingales and Brownian Motion 1996Handbook of Brownian Motion — Facts and Formulae 2002Handbook of Brownian Motion - Facts and Formulae 1993BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES 1967DIFFUSION PROCESSES AND THEIR SAMPLE PATHS 1990The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding 2001Exponential Functionals of Brownian Motion and Related Processes

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