Dynamic Model of Pension Savings Management with Stochastic Interest Rates and Stock Returns

In this review paper we recall a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. The model has been proposed and analyzed by the authors. We assume stock prices to be driven by a geometric Brownian motion whereas interest rates are modeled by means of a one factor interest rate model. It turns out that the optimal decision representing stock to bond proportion is a function of the duration of saving, the level of savings and the short rate. We furthermore summarize the results of testing the model on the fully funded second pillar of the Slovak pension system