We study strong asymptotic properties of two types of integral functionals of geometric stochastic processes. These integral functionals are of interest in financial modelling, yielding various option pricings, annuities, etc., by appropriate selection of the processes in their respective integrands. We show that under fairly general conditions on the latter processes the logs of the integral functionals themselves asymptotically behave like appropriate sup functionals of the processes in the exponents of their respective integrands. We illustrate the possible use and applications of these strong invariance theorems by listing and elaborating on several examples.

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Keywords Black-Scholes financial model, Geometric Brownian motion, Geometric fractional Brownian motion, Geometric Gaussian and diffusion process, Geometric processes, Integral and sup functionals, LIL and strong increments, Strong invariance, Strong theorems
Persistent URL dx.doi.org/10.1017/S0021900200015667
Journal Journal of Applied Probability
Csáki, E. (Endre), Csörgo, M, Földes, A. (Antónia), & Révész, P. (Pál). (2000). Asymptotic properties of integral functionals of geometric stochastic processes. Journal of Applied Probability, 37(2), 480–493. doi:10.1017/S0021900200015667