Insurance and Asymmetric Ambiguity: on the Role of the Insurance Contract as an Informational Transmission Mechanism.

We develop a model of insurance with an informational asymmetry be-tween the insurer and the policy holder that amounts to the inability of the policy holder to assign a unique probability distribution to the relevant events. We show that this asymmetric ambiguity influences the choices of the contracting parties. In fact, the contract itself has potential to reveal information to the contracting party that has the least information: the insured.We observe however, that when the insurer has better quality of in-formation it is indeed better not to disclose this information. This happens through offering the contract it would offer as if it were to be as ambiguous about the probability distribution as the agent. The result could povide some intuitive explanation of why insurance companies are very reluctant to show their customers estimates of accident probabilities. We stress that we cannot reinterpret a model with ambiguity as a model with agents using heterogenous priors. The implications of this finding is that we need to be careful when we analyze optimal contracts when uncertainty is present and people display aversion toward it. The very fact that information is channeled through contracts needs to be taken into account by the parties at both end of the contract. ∗Columbia University 1