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A mean-field formulation for multi-period asset-liability mean-variance portfolio selection with probability constraints

This work was partially supported by Research Grants Council of Hong Kong under grants 519913, 15209614 and 15224215, grants of National Natural Science Foundation of China(No. 11571124 and No. 11671158), and China Postdoctoral Science Foundation (No. 2016M592505).
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  • This paper is concerned with studying an optimal multi-period asset-liability mean-variance portfolio selection with probability constraints using mean-field formulation without embedding technique. We strictly derive its analytical optimal strategy and efficient frontier. Numerical examples shed light on efficiency and accuracy of our method when dealing with this class of multi-period non-separable mean-variance portfolio selection problems.

    Mathematics Subject Classification: Primary: 90C15; Secondary: 91B30.


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  • Figure 1.  Efficient frontiers with different correlation coefficients

    Table 1.  Data for the asset allocation example

    SP EM MS liability
    Expected return 14% 16% 17% 10%
    Standard deviation 18.5% 30% 24% 20%
    Correlation coefficient
    SP 1 0.64 0.79 $\rho_1$
    EM 0.64 1 0.75 $\rho_2$
    MS 0.79 0.75 1 $\rho_3$
    liability $\rho_1$ $\rho_2$ $\rho_3$ 1
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