An Explicit Solution for a Portfolio Selection Problem with Stochastic Volatility

Abstract

In this paper, we revisit the optimal consumption and portfolio selection problem for an investor who has access to a risk-free asset (e.g. bank account) with constant return and a risky asset (e.g. stocks) with constant expected return and stochastic volatility. The main contribution of this study is twofold. Our first objective is to provide an explicit solution for dynamic portfolio choice problems, when the volatility of the risky asset returns is driven by the Ornstein-Uhlenbeck process, for an investor with a constant relative risk aversion (CRRA). The second objective is to carry out some numerical experiments using the derived solution in order to analyze the sensitivity of the optimal weight and consumption with respect to some parameters of the model, including the expected return on risky asset, the aversion risk of the investor, the mean-reverting speed, the long-term mean of the process and the diffusion coefficient of the stochastic factor of the standard Brownian motion.