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Explicit Formulas for Laplace Transforms of Stochastic Integrals

by Tom R. Hurd of McMaster University, and
Alexey Kuznetsov of McMaster University

July 3, 2006

Abstract: In this article we provide a general identity useful for computing expectations of the form

for diffusion processes X t and certain functions Φ. In the case of CIR and Jacobi diffusions, this identity leads to explicit formulas for the Laplace transform of a multidimensional family of random variables constructed from X t and its integrals.

AMS Classification: 60G09, 91B28.

Keywords: diffusions, Laplace transform, explicit formula, hypergeometric function, CIR process, Jacobi process, mathematical finance.

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