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...[ Read more ]

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.