Robust reinsurance and investment strategies under principal–agent framework

In this paper, a class of reinsurance contracting problems is examined under a continuous-time principal–agent framework with mean-variance criteria, where a reinsurer and an insurer are assigned the roles of the principal and the agent, respectively. Both parties can manage their insurance risk by investing in a financial portfolio comprising a risk-free asset and a risky asset. It has been assumed that both the insurer and the reinsurer are concerned about model uncertainty and that they aim to find a robust reinsurance contract and robust investment strategies by maximizing their respective mean-variance cost functionals taking sets of probability scenarios into account. To articulate the time-inconsistency issue attributed to the mean-variance optimization criteria, the optimization procedure of each decision-maker has been formulated as a non-cooperative game and discussed by using an extended HJB equation, which is consistent with the extant work on time-consistent control. Moreover, explicit expressions for the robust reinsurance contract, the robust investment strategies and the value functions of the insurer and reinsurer have been obtained and presented. The numerical results and their economic interpretations are then discussed.