Based On The Jump - Diffusion Model Of Optimal Investment Strategy

X.Y. Zhou and D.Li, in 2000, studied the optimal portfolio selection problem by virtue of stochastic linear-quadratic control theory when the asset price process satisfying a diffusion stochastic differential equation, and obtained the efficient frontier for this portfolio selection problem.Following the work of X.Y. Zhou and D. Li, we pay our attention on the optimal portfolio selection problem when the price process satisfying a jump-diffusion stochastic differential equation.Analogy to the research of X.Y. Zhou and D. Li, we use the Ito formulation to decompose the jump in the price process into two parts:a deterministic part and a stochastic part (realistic situation). In order to maximize its investment returns and to minimize the risk, we adopt to combine these two objective functions into a linear single objective function by putting weights on the two criteria. We also get an analytic solution of the optimal control problem by using the stochastic linear-quadratic method. Similarly, we arrive at the efficient frontier of the optimal portfolio selection problem posed in the present paper, too. The conclusions obtained here can be regarded as a natural generalization to the work of X.Y. Zhou and D.Li.