Insurance Contracts with Adverse Selection When the Insurer Has Ambiguity about the Composition of the Consumers

In this paper, we consider the optimal contract in a monopolistic insurance market when the insurer has ambiguity about the composition of the consumers. When there are only two types of consumers, we find that high-risk consumers are fully insured, whereas low-risk consumers are only partially insured. For an ambiguity averse insurer, as ambiguity increases, the optimal menu of contracts moves toward the one that equalizes the profits earned by the insurer from the two types of consumers. The insurer may offer the same menu of contracts even if her prior belief changes. For an ambiguity seeking insurer, when the degree of ambiguity increases, the optimal menu moves away from the menu that equalizes the profits earned from the two types of consumers.