# American Institute of Mathematical Sciences

January  2018, 14(1): 249-265. doi: 10.3934/jimo.2017045

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

 1 School of Mathematical Sciences, South China Normal University, Guangzhou 51061, China 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China 3 Department of Finance and Investment, Sun Yat-Sen Business School, Sun Yat-Sen University, Guangzhou 510275, China

Received  March 2016 Revised  February 2017 Published  April 2017

Fund Project: 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).

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.

Citation: Xianping Wu, Xun Li, Zhongfei Li. A mean-field formulation for multi-period asset-liability mean-variance portfolio selection with probability constraints. Journal of Industrial & Management Optimization, 2018, 14 (1) : 249-265. doi: 10.3934/jimo.2017045
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##### References:
Efficient frontiers with different correlation coefficients
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
 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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