This article presents a two-period asymmetric learning model of insurance markets. When information about past accidents is not shared by insurers, asymmetries of information develop through time. Equilibrium contracts exist, are payoff unique, and display a realistic bonus-malus pattern. Eliminating asymmetries through information sharing is welfare decreasing, in contrast with past contributions on insurance and adverse selection. When second-period contract offers cannot be contingent on initial contract choice, a strict increase in welfare is obtained through menus of contracts, although initial contract choice is in itself worthless information.