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.

We investigate a robust optimal reinsurance-investment problem for $n$ insurers under multiple interactions, which arise from the insurance market, the financial market, the competition mechanism and the cooperation mechanism. Each insurer's surplus process is assumed to follow a diffusion model, which is an approximation of the classical Cramér-Lundberg model. Each insurer is allowed to purchase proportional reinsurance to reduce their claim risk. To reflect the first moment and second moment information on claims, we use the variance premium principle to calculate reinsurance premiums. To increase wealth, each insurer can invest in a financial market, which includes one risk-free asset and $n$ correlated stocks. Each insurer wants to obtain the robust optimal reinsurance and investment strategy under the mean-variance criterion. By applying a stochastic control technique and dynamic programming approach, the extended Hamilton-Jacobi-Bellman (HJB) equation is established. Furthermore, we derive both the robust optimal reinsurance-investment strategy and the corresponding value function by solving the extended HJB equation. Finally, we present numerical experiments, which yield that competition and cooperation have an important influence on the insurer's decision-making.