We extend the model of ex-ante asymmetric information in the insurance market of Stiglitz (1977) by incorporating consumers’ reactions to uncertainty. Specifically, we assume that some agents are able to assign a precise probability measure to the event of loss (Savage, 1954), whilst others are not. The behavior of the latter group complies either with proba-bilistic sophistication or ambiguity aversion as modeled by maxmin expected utility (Gilboa and Schmeidler, 1989). When the former class exhibits sufficient pessimism, these two types are virtually indistinguishable when exposed to rare hazards. Thus, pooling constitutes as an optimal solution to the problem of the monopolist.