Equilibrium in Insurance Markets With Adverse Selection When Insurers Pay Policy Dividends

We show that an equilibrium always exists in the Rothschild-Stiglitz insurance market model with adverse selection and an arbitrary number of risk types, when insurance contracts include policy dividend rules. The Miyazaki-Wilson-Spence state-contingent allocation is an equilibrium allocation (defined as a set of type-dependent lotteries sustained at a symmetric equilibrium of a market game), and it is the only one when out-of-equilibrium beliefs satisfy a robustness criterion. It is shown that stock insurers and mutuals may coexist, with stock insurers offering insurance coverage at actuarial price and mutuals cross-subsidizing risks.