Mean-Variance Asset-Liability Management in a Non-Markovian Regime-Switching Jump-Diffusion Market with Random Horizon

Abstract

This paper investigates the problem of mean-variance asset-liability management (ALM) in a market where the dynamics of assets are non-Markovian regime-switching models driven by a Brownian motion, a Poisson random measure and a continuous time finite-state Markov chain. It is assumed that the time horizon is uncertain relying not only on asset prices and liability values, but also on other factors. The insurer aims to minimize the variance of the terminal surplus given an expected terminal surplus subject to the risk of paying out random liabilities of an extensive Cramer-Lundberg model. By further developing the solvability of a linear backward stochastic differential equation (BSDE) with two types of jumps, namely jumps modelled by a Poisson random measure and by basic martingales related to a Markov chain, closed-form expressions for both the efficient strategy and the efficient frontier are obtained and represented by unique solutions to several relevant BSDEs.