Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

This paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained m the case where the SDEs are driven by Browman motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving "noise" are stable processes and Gamma processes are considered. Keywords: Levy process; Browman motion; stochastic investment model