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Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation

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3 Author(s)
Shu-Shang Zhu ; Dept. of Manage. Sci., Fudan Univ., Shanghai, China ; Duan Li ; Shou-yang Wang

For an investor to claim his wealth resulted from his multiperiod portfolio policy, he has to sustain a possibility of bankruptcy before reaching the end of an investment horizon. Risk control over bankruptcy is thus an indispensable ingredient of optimal dynamic portfolio selection. We propose in this note a generalized mean-variance model via which an optimal investment policy can be generated to help investors not only achieve an optimal return in the sense of a mean-variance tradeoff, but also have a good risk control over bankruptcy. One key difficulty in solving the proposed generalized mean-variance model is the nonseparability in the associated stochastic control problem in the sense of dynamic programming. A solution scheme using embedding is developed in this note to overcome this difficulty and to obtain an analytical optimal portfolio policy.

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Automatic Control, IEEE Transactions on  (Volume:49 ,  Issue: 3 )