Optimal combination of quota-share and stop-loss reinsurance treaties under the joint survival probability

A reinsurance contract involves two parties: an insurer and a reinsurer. Most existing optimal reinsurance treaties consider only the interest of one party. In this paper, we consider the interests of both the insurer and reinsurer and derive the optimal reinsurance contract in the form of the combination of quota-share and stop-loss reinsurance under the optimization criteria that maximize the joint survival probability. We first study the joint survival probability of insurers and reinsurers. We then derive conditions for the existence of the optimal reinsurance retentions and determine the optimal retentions that maximize the joint survival probability under expected value reinsurance premium principle.