MEAN-VARIANCE ASSET-LIABILITY MANAGEMENT: FROM SURPLUS OPTIMIZATION TO LIABILITY-DRIVEN INVESTMENT

This paper investigates continuous-time intertemporal liabilitydriven investment strategies in the presence of liability constraints in a regimeswitching market. We employ the value of the liability portfolio as a natural numeraire rather than a traditional surplus to study the liability-driven optimal investment using the mean-variance criterion. Using the stochastic linear-quadratic control method, we obtain the closed-form optimal investment strategy and efficient frontiers to this problem. The solution involves a three-fund separation theorem based on investment in two underlying building blocks, the performance seeking portfolio and a liability hedging portfolio, in addition to the risk-free asset. That provides formal justification for liabilitydriven investment solutions offered by investment banks, insurance companies, and asset management firms under regime-switching environment. The optimal allocation strategy has a distinct cross-regime effect, both in terms of the components of the optimal allocation and their weights. Finally, the numerical analysis shows that the larger the initial asset-liability ratio and maturity are, the greater the terminal asset-liability ratio under the same risk level. The effects of parameters on liability-driven investment strategies vary according to different market states. Expected asset-liability structure, self-owned assetliability structure, time horizon, and the transition rate from a bearish to a bullish regime have a more significant impact on optimal portfolio allocation in a bearish regime than in a bullish regime. The asset-liability structure is more vulnerable to fluctuations in a bearish market than in a bullish market.