  Exponential functionals of Brownian motion have been extensively studied in
financial and insurance mathematics due to their broad applications, for
example, in the pricing of Asian options. The Black-Scholes model is appealing
because of mathematical tractability, yet empirical evidence shows that
geometric Brownian motion does not adequately capture features of market equity
returns. One popular alternative for modeling equity returns consists in
replacing the geometric Brownian motion by an exponential of a Levy process. In
this paper we use this latter model to study variable annuity guaranteed
benefits and to compute explicitly the distribution of certain exponential
functionals.
