Abstract: This paper discusses the robust asset-liability management problem of maximizing the expected utility of the terminal wealth under partial information with delay, that is, the investors can observe the risky asset price with random drift which is not directly observable in the financial market. It is reduced to a partially observed stochastic differential game problem. This paper tries to an effort to find the equilibrium strategies by maximizing the expected utility of the insurer's terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of filtering theory and the dynamic programming approach, we derive the robust equilibrium strategies and value functions explicitly. Finally, some numerical examples are presented. Obviously, the value function is higher in the full information case than it in the partial information case. Therefore, investors should collect more information related to investment as much as possible in order to make more informed decisions.

Key words: robust equilibrium strategies, filtering theory, delay, utility maximization, partial information