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This paper considers a state-dependent optimal asset-liability management problem in continuous-time settings. The investor maximizes the expected state-dependent utility of the terminal asset-liability ratio in a regime-switching market to better describe insurance companies’ needs for asset-liability matching and regulation with background risk. We apply the stochastic dynamic programming method to get closed-form results. We find that the optimal strategy in the state-dependent utility case is the same, and the optimal value function differs from the state-independent utility case. Finally, we study how the parameters impact the optimal investment strategy and corresponding value functions through numerical examples.

Asset-liability management with state-dependent utility in the regime-switching market