Given that, in equilibrium, all agents freely opt for strictly positive own coverage, competitive models of asymmetric information predict a positive relationship between coverage and ex post risk (accident probability). On the other hand, some recent empirical studies find either negative or no correlation. This paper, by introducing heterogeneity in risk perceptions into an asymmetric information competitive model, provides an explanation to this puzzle. The more optimistic agents underestimate their accident probability relative to less optimistic and so purchase less insurance. They also tend to be less willing to take precautions. This gives rise to separating equilibria exhibiting negative or no correlation between coverage and ex post risk that potentially explain the puzzling empirical findings. Moreover, the no-correlation equilibrium involves some agents being quantity-constrained due to adverse selection. Thus, although the no-correlation empirical findings indicate that there may not be risk-related adverse selection, they do not imply the absence of other forms of adverse selection that have significant effects on the resulting equilibrium.
