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

Xianping Wu; Xun Li; Zhongfei Li

doi:10.3934/jimo.2017045

Article Contents

2018, Volume 14, Issue 1: 249-265. Doi: 10.3934/jimo.2017045

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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

Early access: April 2017

Published: January 2018

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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Abstract

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.

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

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Figure 1. Efficient frontiers with different correlation coefficients

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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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