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Mathematical Problems in Engineering
Volume 2014, Article ID 140140, 9 pages
http://dx.doi.org/10.1155/2014/140140
Research Article

Continuous-Time Mean-Variance Asset-Liability Management with Hidden Markovian Regime Switching

Department of Economic and Trade, Guangdong University of Finance, Guangzhou 510521, China

Received 13 February 2014; Accepted 22 May 2014; Published 15 June 2014

Academic Editor: Piermarco Cannarsa

Copyright © 2014 Ling Zhang. 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.

Abstract

This paper considers a continuous-time mean-variance asset-liability management problem with incompletely observable information. An investor can only observe the prices of the asset and liability and the dynamics of the unobservable states of the underlying financial market is described by a hidden Markovian chain. The price of the risky asset is assumed to be governed by a hidden Markovian regime switching geometric Brownian motion and the liability is assumed to follow a hidden Markovian regime switching Brownian motion with drift, respectively. The appreciation rates of the risky asset and the liability are modulated by the hidden Markovian chain. By using the separation principle, the filtering-estimation problem and the mean-variance asset-liability management problem are discussed. The explicit expressions for the optimal asset-liability management strategy and the mean-variance efficient frontier are determined by using the stochastic maximum principle.