Reciprocal Reinsurance Treaties Under an Optimal and Fair Joint Survival Probability

In this paper, we study reinsurance treaties between an insurer and a reinsurer, considering both parties’ interests. Most papers only focus on the insurer’s point of view. The latest research considering both sides has considerably oversimplified the joint survival function. This situation leads to an unrealistic optimal solution; one of the parties can make risk-free profits while the other bears all the risk. Here, we define and optimize a fair joint survival probability for a reciprocal reinsurance treaty, under the expected value principle, for both quota-share and stop-loss reinsurance contracts.