Optimal Portfolio and Consumption Policies with Stochastic Volatility

Abstract

Optimal asset allocation and consumption policies have been important issues in finance in the past decades. We study these issues under constant relative risk aversion (CRRA) utility functions in a general setting: stochastic volatility, incomplete markets and finite investment horizons. So far, numerical computation has been the main method for obtaining solutions in this general setting. We present a closed-form approximate solution for this dynamic optimization problem. We show that our theoretical predictions are in good agreement with numerical results and our approximation error is even smaller than the parameter-estimation errors in underlying dynamics.