Optimales Vertragsdesign bei moralischem Risiko in der Rückversicherung

This paper addresses the optimal design of risk sharing arrangements in reinsurance contracts with asymmetric information concerning the primary insurer’s behavior. The latter usually has significant unobservable discretions, for instance with respect to risk selection, implying a moral hazard problem. We show that the existence of moral hazard strongly affects the characteristics of the reinsurance indemnification rule, i. e. the connection between the level of losses and the indemnity, which is specified in the contract. For this analysis, a standard model framework from the theory of optimal reinsurance with perfect information is modified by the assumption that the primary insurer has unobservable control of the probability distribution of the extent of losses. In particular, the solution indicates that for this situation, a Pareto-optimal indemnity rule is less steep, and therefore the primary insurer’s share in a marginal increase of the loss is greater, compared to the case of complete information. A deductible, however, turns out not to be a suitable approach in this context.