Mean-variance portfolio selection with only risky assets under regime switching

This paper explores a portfolio selection model of multiple risky assets with regime switching. There are n+1 risky assets in the financial market available to the mean-variance investors. The feasibility issue is solved by constructing an equivalent condition. We derive the analytical expressions of the efficient frontier and efficient feedback portfolio via three systems of ordinary differential equations that admit unique solutions. The mutual fund theorem is also proved. Several numerical examples are provided to demonstrate how the efficient frontier is affected by the market regime movement and the investor's time horizon.