Optimal consumption and portfolio selection problem : the martingale approach

Abstract

This paper applies Cox-Huang [2] martingale method to solve the optimal portfolio-selection and consumption problem. The model assumes that an investor, who has an initial wealth W0, needs to maximize his utility of consumption and of final wealth by making his consumption and portfolio-selection decisions continuously during the lifetime. As a test case, the optimal solution for the basic two-asset problem when the risky asset price follows geometric Brownian motion is obtained. More importantly, I derive the explicit solution for the multi-asset problem in the infinite time horizon case when the prices of the risky assets follow the mean reverting returns processes. The result is consistent with Merton’s result [7] on two-asset case. Furthermore, the case of risky assets follow the so called norm-price level hypothesis is also considered with analytical solution derived.

Date of Award	2002
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology