Mean-Variance Portfolio Selections in Continuous-Time Mode with Poisson Jumps

Within Markowitz´s mean-variance framework, the portfolio selection problem is proposed on finite time horizon [0,T] . Unlike with the classical continuous-time mean-variance portfolio selection, the stocks´ price processes satisfy stochastic differential equations with poisson jumps, and the interest rate is stochastic process. By using stochastic analyze theory and backward stochastic differential equation´s theory, the formula of the efficient investment portfolio is obtained. Furthermore, the efficient frontier of mean-variance portfolio selection was also obtained explicitly in a closed form.