Yes, No, Perhaps? - Explaining the Demand for Risk Classification Insurance with Fuzzy Private Information

We examine the demand for risk classification insurance with fuzzy private information using an expected utility set-up. We first demonstrate that standard assumptions on private information cannot explain the observed demand for risk classification insurance. By allowing for fuzzy heterogeneous private information, we show that a unique equilibrium exists that can be of the form that some of the individuals buy risk classification insurance while others do not, as observed in real-life insurance markets. We derive a condition for the existence of such an equilibrium and show that this is particularly driven by the risk attitude of the insured, the volatility of outcomes without risk classification insurance and the distribution of information. We also make welfare comparisons and show that in the case of multiple equilibrium candidates the one with the highest portion of risk classification insurance buyers is Pareto superior and, thus, the unique equilibrium.