Explicit Formulas for Laplace Transforms of Stochastic Integrals

#### T.R. Hurd, A. Kuznetsov

2008, v.14, Issue 2, 277-290

ABSTRACT

In this article we investigate some applications of a general measure change identity for expectations of the form \begin{align*} E \bigg[ \exp \bigg( -\int\limits_0^T \phi(X_s) \, ds \bigg) g(X_{T} ) \bigg] \end{align*} for diffusion processes $X_t$ and certain functions $\phi$. In the case of Cox-Ingersoll-Ross (CIR) and Jacobi diffusions, two families of processes often applied in mathematical finance, this identity leads to explicit formulas for the Laplace transform of an important multidimensional family of random variables constructed from $X_t$ and its integrals. Our results extend the range of applicability of these diffusions in finance.

Keywords: Markov diffusions,Laplace transform,Girsanov theorem,hypergeometric functions,CIR process,Jacobi process,mathematical finance