A Stochastic Investment Model on a Finite Time Horizon

In this paper,we consider an investment optimization problem on a finite time horizon.One risky and one riskless asset are considered,and transaction costs are ignored.The risky asset prices obey a logarithmic Brownian motion,and interest rates vary according to a Vasicek interest rate model.The goal is to choose optimal investment policies to maximize the expected Hyperbolic Absolute Risk Aversion(HARA)utility of final payoff(wealth).The problem is then reduced to a 1-dimensional stochastic control problem by virtue of the Girsanov transformation.A dynamic programming principle is used to derive the dynamic programming equation(DPE).Explicit solutions are derived under certain conditions.The solutions are then used to derive the optimal investment strategy.