Optimal Investment and Consumption Decisions Under the Ho-Lee Interest Rate Model

In this paper, we consider an investment and consumption problem with stochastic interest rate, in which risk-free interest rate dynamics is driven by the Ho-Lee model,while risky asset price is supposed to follow a geometric Brownian motion and be correlated with interest rate dynamics. Our goal is to seek an optimal investment and consumption strategy to maximize the expected discounted utility of consumption and terminal wealth in the finite horizon. Firstly, we apply dynamic programming principle to derive Hamilton-Jacobi-Bellman(HJB) equation for the value function and take power utility and logarithm utility for our analysis. Secondly, by conjecturing the form of a solution and solving partial differential equations, we obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to demonstrate the impact of market parameters on the optimal investment and consumption strategy. Key–Words: Investment and consumption problem; the Ho-Lee model; dynamic programming principle; HJB equation; closed-form solution;