Markowitz's mean-variance asset-liability management with regime switching: A time-consistent approach

In this article, we provide the first study in the time consistent solution of the mean-variance asset liability-management (MVALM). The framework is even considered under a continuous time Markov regime-switching setting. Using the extended Hamilton-Jacobi-Bellman equation (HJB) (see Bjork and Murgoci (2010)), we show that the time consistent equilibrium control is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the similar problem in Bjork and Murgoci (2010), in which it is independent of the state. Finally, we give a numerical comparison between our work with the corrected version (as obtained here) of pre-commitment strategy in Chen et al. (2008). Crown Copyright (c) 2013 Published by Elsevier B.V. All rights reserved.