This talk is based on a forthcoming paper by E. Csaki, M. Csorgo, A. Foldes and P. Revesz, where we study strong asymptotic properties of two types of integral fuctionals of geometric stochastic processes. These integral functionals are of interest in financial modeling, yielding various Asian type option pricings via appropriate selection of the processes in their respective integrands. We show that, under fairly general conditions on the latter processes, the log of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. In addition to presenting these theorems in their general form, we will also illustrate them via geometric Brownian and geometric fractional Brownian motions.