Effect of Correlation of Brownian Motions on an Investor,s Optimal Investment and Consumption Decision under Ornstein-Uhlenbeck Model

The aim of this paper is to investigate and give a closed form solution to an investment and consumption decision problem where the risk-free asset has a rate of return that is driven by the Ornstein-Uhlenbeck Stochastic interest rate of return model. The maximum principle is applied to obtain the HJB equation for the value function. Owing to the introduction of the consumption factor and the Ornstein-Uhlenbeck Stochastic interest rate of return, the HJB equation derived becomes much more difficult to deal with than the one obtained in literature. In the same spirit with the techniques literature, the nonlinear second-order partial differential equation was transformed into an ordinary differential equation; specifically, the Bernoulli equation, using elimination of dependency on variables for easy tackling.