Mean-variance Portfolio Model with Consumption

Suppose that a market consists of a foreign exchange deposit and a risky stock, the optimal portfolio problem with consumption is formulated under the continuous-time mean- variance frame. By using the stochastic linear-square control theory, the explicit optimal trading strategies and the closed-form efficient frontier are derived. The numerical example shows that with the increase of the consumption rate, the amount invested in the risky stock, the mean terminal wealth, and the variance of the terminal wealth are all decreased.