We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (chance of a loss) is private information, a problem introduced in Stiglitz (1977)'s seminal paper. We prove several properties of optimal menus: the highest type gets full coverage (efficiency at...

We solve the principal-agent problem of a monopolist insurer selling to an agent whose riskiness (loss chance) is private information, a problem introduced in Stiglitz's (1977) seminal paper. For an \emph{arbitrary} type distribution, we prove several properties of optimal menus, such as...

Models of insurance with adverse selection predict that only the best risks — those least likely to suffer a loss — are uninsured, a prediction at odds with coverage denials for pre-existing conditions. They also typically assume that insurance pro- vision is costless: the only cost is...