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-WilsonSpence state-contingent allocation is an equilibrium allocation, 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 o⁄ering insurance coverage at actuarial price and mutuals cross-subsidizing risks