On Optimal Reinsurance Treaties in Cooperative Game under Heterogeneous Beliefs

In this paper, we study the optimal reinsurance policies as the result of a two-person cooperative game, where both parties in the negotiation are risk averse and are trying to maximize their expected utility. We incorporate information asymmetry by assuming that the insurer and the re-insurer have different beliefs on the distribution of the underlying losses. Our analysis consists of two parts. The first part deals with the situation when the reinsurance premium is fully negotiable; whereas the second part deals with the situation when the premium is determined by an actuarial premium principle. For both parts, we first derive the Pareto-optimal reinsurance contracts, then the reinsurance contracts in the Nash equilibrium as well as in the Kalai-Smorodinsky equilibrium are identified