The Design of Optimal Policies with Layers: Implications for Catastrophe Reinsurance

Abstract

This paper examines the optimal form of layered excess-of-loss (XOL) reinsurance contracts. The presence of layers creates incompleteness in the sense that it leads to market segment. Segmentation of markets causes some barriers to risk sharing between insurers and reinsurers. These barriers create an incentive for the insurer to adopt an optimal policy with layers to reduce their negative effects. Under the mean-variance framework, we find that the role of covariance between layers is crucial in determining the optimal reinsurance form. We prove that the optimal layered XOL contract consists of deductibles, jumps, as well as parts of full coverage. Because the jumps in the optimal layered XOL contract may cause severe moral hazard problem, we then turn to studying two modified classes of reinsurance contracts, in which jumps are forbidden. The problem of optimal layering is also considered for catastrophe reinsurance.