We study a generalization of the classical monopoly insurance problem under adverse selection (see Stiglitz 1977) where we allow for a random distribution of losses, possibly correlated with the agent’s risk parameter that is private information. Our model explains patterns of observed customer behavior and predicts insurance contracts most often observed in practice: these consist of menus of several deductible-premium pairs or menus of insurance with coverage limits–premium pairs. A main departure from the classical insurance literature is obtained here by endowing the agents with risk-averse preferences that can be represented by a dual utility functional (Yaari 1987).
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* Gershkov: Department of Economics and the Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, and School of Economics, University of Surrey (email: firstname.lastname@example.org); Moldovanu: Department of Economics, University of Bonn (email: email@example.com); Strack: Department of Economics, Yale University (email: firstname.lastname@example.org); Zhang: Department of Economics, University of Bonn (email: email@example.com). Jeff Ely was the coeditor for this article. We wish to thank the coeditor and three anonymous referees for their many editorial suggestions. We also wish to thank Emre Özdenoren, Ian Jewitt, Andreas Kleiner, Martin Pollrich, Uzi Segal, and Ming Yang for helpful remarks. Gershkov wishes to thank the Israel Science Foundation grant 1118/22 for financial support. Moldovanu and Zhang acknowledge financial support from the DFG (German Research Foundation) via Germany’s Excellence Strategy—EXC 2047/1-390685813, EXC 2126/1-390838866, and the CRC TR-224 (project B01). Strack was supported by a Sloan Fellowship.
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