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

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 dynamicsof the unobservable states of the underlying financial market is described by a hidden Markovianchain. The price of the risky asset is assumed to be governed by a hidden Markovianregime switching geometric Brownian motion and the liability is assumed to follow a hiddenMarkovian regime switching Brownian motion with drift, respectively. The appreciation rates ofthe risky asset and the liability are modulated by the hidden Markovian chain. By using theseparation principle, the filtering-estimation problem and the mean-variance asset-liabilitymanagement problem are discussed. The explicit expressions for the optimal asset-liabilitymanagement strategy and the mean-variance efficient frontier are determined by using thestochastic maximum principle