An Option-Based Approach to Determining the Optimal Reinsurance Stop-Loss Premium

This paper uses option-pricing theory to develop a model for determining the optimal reinsurance premium to be charged by the reinsurer to the primary insurer in a nonproportional stop-loss reinsurance treaty. A discussion of several reinsurance contracts is also presented. It is found that the fair reinsurance premium is given by the weighted sum of the level of claims plus the present value of the maximum payoff to the reinsured less the present value of the reinsured's retention limit. The fair reinsurance premium increases in the maximum amount to be paid by the reinsurer, decreases in the retention limit, and is nonmonotonic in the volatility of underlying claims