Pricing the Impact of Adjustable Features and Loss Sharing Provisions of Reinsurance Treaties

Excess-of-loss reinsurance contracts often contain loss sharing provisions, such as aggregate deductibles, loss ratio caps or limited reinstatements, and loss corridor provisions. They also frequently contain adjustable premium or commission features, such as retrospective rating plans, profit commission plans, and sliding scale commission plans. Pro rata treaties frequently contain adjustable commission features. This paper presents an overview of two approaches to pricing aggregate loss distribution problems: the lognormal model and the Heckman-Meyers Collective Risk Model. Applications to reinsurance pricing are then presented. Finally, the paper compares results of applying these approaches to representative working excess-of-loss treaties. These comparisons suggest that the lognormal model can provide satisfactory approximations to the theoretically more appropriate Collective Risk Model when use oft he latter more sophisticated procedure is not necessary due either to data limitations or to the influence of market conditions and negotiations. The increased efficiency of the lognormal model can lead to greater accuracy by making judgmental estimates unnecessary in many situations. The basic lognormal model is generally applicable to pro rata treaties and working excess-of-loss treaties. A mixture of lognormal and discrete distributions is presented that may be applicable in many low mean frequency situations. Cash flow modeling is also discussed.