Risk Sharing with Multiple Indemnity Environments

Optimal risk sharing arrangements have been substantially studied in the literature, from the aspects of generalizing objective functions, incorporating more business con- straints, and investigating different optimality criteria. This paper proposes an insur- ance model with multiple risk environments. We study the case where the two agents are endowed with the Value-at-Risk or the Tail Value-at-Risk, or when both agents are risk-neutral but have heterogeneous beliefs regarding the underlying probability distribution. We show that layer-type indemnities, within each risk environment, are Pareto optimal, which may be environment-specific. From Pareto optimality, we get that the premium can be chosen in a given interval, and we propose to allocate the gains from risk sharing equally between the buyer and seller.