Selection of an optimal portfolio with stochastic volatility and discrete observations

Abstract

We give a numerical method to calculate the optimal self-financing portfolio of stock and risk-free asset to maximize the wealth's expected future utility, in the case of stochastic volatility and discrete observations: the portfolio stock allocation is only allowed to change discretely in time at fixed time intervals. We use a particle-filtering and Monte-Carlo-type algorithm, which we implement forward in time in the case of power utility.