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Mathematical Problems in Engineering
Volume 2015, Article ID 687428, 16 pages
Research Article

A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

1School of Economics, Southwest University for Nationalities, Chengdu, Sichuan 610041, China
2School of Finance and Statistics, Hunan University, Changsha, Hunan 410079, China
3Business School, Sichuan University, Chengdu, Sichuan 610064, China
4Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 15 May 2015; Accepted 6 September 2015

Academic Editor: Leonid Shaikhet

Copyright © 2015 Hui-qiang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.