Pareto Optimal Insurance Policies: Kinks with or without frictions

Abstract

We analyze optimal risk sharing between a customer and an in surer, and present alternative explanations for the prevalence of kinks in Pareto optimal contracts, like deductibles and upper bounds as in XL-contracts. Linear indemnity functions have primarily been considered in the literature. We focus on nonlinear contracts, which can be explained on the basic of different preferences held by the parties involved. In this setting we derive Pareto optimal contracts with ”near” deductibles and ”near’ caps, which we illustrate by examples. Lastly we consider a model based on non-verifiability where the insurer is risk-neutral. We change to a setting where both the cedent and the reinsurer are strictly risk averse. This rationalizes both an endogenous upper cap and a deductible, retaining compensations for risk bearing.