Robust optimal reinsurance strategy with correlated claims and competition

This paper investigates the robust optimal reinsurance strategy, which simultaneously takes into account the ambiguity aversion, the correlated claims and the joint interests of an insurer and a reinsurer. The correlated claims mean that future claims are correlated with historical claims, which are measured by an extrapolative bias. The joint interests of the insurer and the reinsurer are reflected by the competition between them. To better reflect competition, we assume that the insurer and the reinsurer are engaged in related insurance business. The insurer is allowed to purchase proportional reinsurance or acquire a new business. Under ambiguity aversion and the criterion of maximizing the expected utility of terminal wealth, we obtain explicit solutions for the robust optimal reinsurance strategy and the corresponding value function by using the stochastic dynamic programming approach. Furthermore, we obtain the optimal reinsurance strategy under four typical cases. A series of numerical experiments were carried out to illustrate how the robust optimal reinsurance strategy varies with model parameters, and the result analyses reveal some interesting phenomena and provide useful guidance for reinsurance in reality.