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...