Availability crises in insurance markets: Optimal contracts with asymmetric information and capacity constraint

Abstract

Insurance markets sometimes exhibit "crises" in which prices rise dramatically and coverage is unavailable or is rationed at the new prices. A recent explanation for such crises is the "capacity constraint" model of Gron and Winter. Crises usually follow sudden and large depletions in insurers' equity or surplus. The capacity constraint model argues that frictional costs in replacing surplus, and limited liability, give rise to a kinked insurance supply function and that crises arise from discontinuous short term adjustments around the kink. While this model explains much about liability insurance crises, it still leaves unexplained their most prominent feature; that insurance is rationed or unavailable. We follow their insight in looking to equity shocks and capital market frictions to explain crises and combine this with a model of optimal risk sharing contracts under the information conditions characteristic of this market. We use implicit long term contracts with truth telling constraints to address information asymmetries and this allows us to model crises that exhibit rationing. Our model is tested in the market most dramatically affected by such crises in the 1980‘s, the general liability insurance market.