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

Abstract EN

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.