Robust optimal investment-reinsurance strategies with the preferred reinsurance level of reinsurer

This paper investigates robust equilibrium investment-reinsurance strategy for a mean variance insurer. With a larger market share, a reinsurer has a greater say in negotiating reinsurance contracts and makes the decision to propose the preferred level of reinsurance and charges extra fees as a penalty for losses that deviate from the preferred level of reinsurance. Once the insurer receives a decision from the reinsurer, the insurer weighs its risk-bearing capacity against the cost of reinsurance in order to find the optimal investment-reinsurance strategy under the mean-variance criterion. The insurer who is ambiguity averse to jump risk and diffusion risk obtains a robust optimal investment-reinsurance strategy by dynamic programming principle. Moreover, the reinsurance strategy is no longer excess-of-loss reinsurance or proportional reinsurance. In particular, the insurer may purchase proportional reinsurance for different ranges of loss and the proportion depends on the extra charge rate, which is more consistent with market practice than the standard excess-of-loss reinsurance and proportional reinsurance. The optimal reinsurance policy depends on the degree of ambiguous aversion to jump risk and not on the degree of ambiguous aversion to diffusion risk. Finally, several numerical experiments are presented to illustrate the impacts of key parameters on the value function and the optimal reinsurance contracts.