The Impact of Consumption on an Investor’s Strategy under Stochastic Interest Rate and Correlating Brownian Motions

In this work, we consider that an investor’s portfolio comprises of two assets- a risk-free asset driven by
Ornstein-Uhlenbeck Stochastic interest rate of return model and the second asset a risky stock with a price
process governed by the geometric Brownian motion. It is also considered that there are withdrawals for
consumption and taxes, transaction costs and dividends are in involved. The aim was to investigate the effect of
consumption on an investor’s trading strategy under correlating Brownian motions. The relating Hamilton-
Jacobi-Bellman (HJB) equation was obtained using maximum principle. The application of elimination of
variable dependency gave the optimal investment strategy for the investor’s problem. Among the findings is that
more fund should be made available for investment on the risky asset when there is consumption to keep the
investor solvent.