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Exponential functionals of Brownian motion have been extensively studied infinancial and insurance mathematics due to their broad applications, forexample, in the pricing of Asian options. The Black-Scholes model is appealingbecause of mathematical tractability, yet empirical evidence shows thatgeometric Brownian motion does not adequately capture features of market equityreturns. One popular alternative for modeling equity returns consists inreplacing the geometric Brownian motion by an exponential of a Levy process. Inthis paper we use this latter model to study variable annuity guaranteedbenefits and to compute explicitly the distribution of certain exponentialfunctionals.

Exponential functionals of Levy processes and variable annuity guaranteed benefits