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.