An investor’s portfolio is considered to comprise two assets-a risk-free asset governed by stochastic interest rate of return and a risky asset that has its price process driven by the geometric Brownian motion in a financial market where consumption, taxes, transaction costs and dividends are charged and paid. The goal is to find the effect of consumption on an investor’s trading strategy under non-correlating Brownian motions. The maximum principle is used to determine the relating Hamilton-Jacobi-Bellman (HJB) equation. On the application of elimination of variable dependency, the investor’s optimal investment strategy was obtained. The findings include that due to consumption more fund is to be invested on the risky asset when there is consumption.
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