Optimal Investment and Consumption Decision for an Investor with Ornstein-Uhlenbeck Stochastic Interest Rate Model through Utility Maximization

摘要

In this work, an investor's portfolio is considered to comprise of two assets: 1) a risky stock, in which the price process is driven by the geometric Brownian motion; and,2) a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aims at the optimization of an investor's expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation [HJB]) was obtained which was reduced to an ordinary differential equation (ODE) by elimination of variables. The solution to the ODE gave the closed form solution of the investor's problem. It was found that the optimal investment in the risky asset is horizon dependent, a ratio of the total amount available for investment, and the relative risk aversion coefficient.