I analyze long-term contracting in insurance markets with asymmetric information. The buyer privately observes her risk type, which evolves stochastically over time. A long-term contract specifies a menu of insurance policies, contingent on the history of type reports and contractable accident information. The optimal contract offers the consumer in each period a choice between a perpetual complete coverage policy with fixed premium and a risky continuation contract in which current period's accidents may affect not only within-period consumption (partial coverage) but also future policies. The model allows for arbitrary restrictions to the extent to which firms can use accident information in pricing. In the absence of pricing restrictions, accidents as well as choices of partial coverage are used in the efficient provision of incentives. If firms are unable to use accident history, longer periods of partial coverage choices are rewarded, leading to menus with cheaper full-coverage options and more attractive partial-coverage options
and allocative inefficiency decreases along all histories. These results are used to study a model of perfect competition, where the equilibrium is unique whenever it exists, as well as the monopoly problem, where necessary and sufficient conditions for the presence of information rents are given.