دانلود رایگان مقاله انتخاب سبد سهام واریانس با دارایی مخاطره آمیز تحت سوئیچینگ رژیم

Abstract

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.

7. Conclusion

This paper studies a continuous time mean-variance portfolio selection problem when the financial market consists of only risky assets whose price processes are modelled by Markov-modulated geometric Brownian motions. By introducing the Lagrange multiplier, the efficient frontier and efficient portfolio are expressed in closed form via three systems of ordinary differential equations. The global minimum variance is obtained, and the mutual fund theorem is proved by the fact that the efficient feedback portfolio is an affine function of the expected wealth level at the terminal time T. A few extensions can be made in our future research. The asset liability management problem could be investigated by taking into account the investor's endogenous or exogenous liability process. Additionally, to reflect limitations in the real market, constraints, such as prohibitions of short-selling the risky assets, may be imposed.