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

Ling Zhang

doi:10.1155/2014/140140

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.

Highlights

Liability has a significant impact on asset allocation for many asset management institutions, like pension fund, bank, and insurance company
This paper considers a continuous-time mean-variance asset-liability management problem with incompletely observable information
Following Elliott et al [17], problem (9) can be decomposed into two separable problems: a filtering-estimation problem in which the investor infers the unobservable model parameters based on the observed information up to that moment and an optimization problem in which the investor uses the current estimates of the unobservable model parameters to determine the optimal asset-liability management strategy

Summary

Introduction

Liability has a significant impact on asset allocation for many asset management institutions, like pension fund, bank, and insurance company. In view of the study of the mean-variance asset-liability management problem with Markovian regime switching, Chen et al [11] extend the model of Xie et al [9] by adding an independent Brownian motion in the evolution of the liability They examine the feasibility of the asset-liability management problem in a continuous-time setting and derive the analytical optimal asset-liability management strategy by using the LQ control. By incorporating liability into the continuous-time meanvariance portfolio optimization problem in a Markovian regime switching market, Xie [12] derives the optimal assetliability management strategy by using the LQ technique and Lagrange multiplier technique. A mean-variance asset-liability management problem is considered in a continuous-time hidden Markovian regime switching market with a risky asset and a riskfree asset.

Hidden Markovian Model with Liability

Separation Principle

The Auxiliary Problem

Special Cases

Conclusion