Study On Optimal Investment Strategy With Declining/Increasing Constrains

According to the rule of our country for security investment, this paper first establishes a price model with return constrains to depict price behavior of risk asset. Then, assume the investor will invest his wealth in a kind of risky assets and a risk-free asset, where the risk-free asset has a constant return and the risky asset’s price follows the established model above. Furthermore, assume that the investor’s objective is to maximize his expected exponential utility or quadratic utility function of his terminal wealth at a fixed terminal time. Using stochastic analysis, optimal investment strategy is obtained. Especially, explicit solutions are obtained for optimal investment strategy with quadratic utility function. Based on the explicit solutions, the influence of each parameter of the optimal dynamic choice is illustrated numerically.