Essays in Insurance and Adverse Selection

I study the design and efficiency of insurance contracts in markets with asymmetric information. The first chapter considers dynamic pricing schemes in insurance markets in which customers have evolving risk-relevant characteristics. The second chapter characterizes equilibria in competitive insurance markets with stochastic contract offers. The last chapter studies optimal selling mechanisms in settings where buyers have information beyond their own valuation for a good. In the first chapter I analyze insurance provision in a dynamic model in the presence of recurrent risks. Hence, it can be to the benefit of the firms and customers to enter long-term contracts. I analyze contracting in insurance markets where customers' risk-relevant characteristics evolve stochastically and are not contractible (e.g., health status in health insurance). In the model considered, firms compete by offering long-term contracts to customers. By breaking each firm's problem into how much utility to provide agents and how to minimize costs, equilibrium is characterized in a tractable way, despite the large set of possible contracts. There exists (at most) a unique equilibrium in which firms make zero profits, whatever the initial type of the customer.;Equilibrium contracts feature a dynamic pricing scheme: in each period the agent chooses between partial coverage and a perpetual complete-coverage insurance policy with a fixed premium. This premium decreases with the amount of time the agent continues to buy partial insurance, which serves as a costly signal of his initial type. With an infinite horizon, all agents purchase full insurance eventually and the long run distribution of premia is described by the distribution of complete insurance purchases. Inefficiency is decreasing along all histories. I also provide necessary and sufficient conditions for equilibrium existence and show that the qualitative properties of contracts extend to the monopoly setting. These results provide new implications of asymmetric information for pricing and coverage in insurance markets.;The second chapter studies subgame perfect equilibria in the competitive insurance model of Rothschild and Stiglitz (1976). A finite number of firms compete by offering menus of contracts to an agent whose risk characteristics are private information. In the game considered, equilibrium existence follows from the seminal results of Dasgupta and Maskin (1986). I go beyond existence, showing that there is a unique symmetric equilibrium and characterizing its properties. The equilibrium is outcome-equivalent to the competitive equilibrium presented by Rothschild and Stiglitz, whenever the latter exists. Otherwise, the equilibrium features randomization over a range contract menus that exhibit cross-subsidization. Strategies and welfare are continuous and monotone in the prior distribution over types, and the outcome converges to the perfect information allocation when the prior approaches its extreme values. Such continuity is absent in alternative models of competitive insurance in the literature.;On the last chapter, I characterize revenue-maximizing mechanisms in auction settings with `rich' type spaces, where bidders obtain information from sources other than their own valuation. By considering a relaxed problem, I provide an upper bound on revenue extraction that explicitly builds on the richness of the information structure. I provide a condition under which this upper bound is achieved and describe an optimal mechanism. Under this condition, I also show that the optimal revenue can be achieved through dominant strategy implementation. The optimal revenue result generalizes the full surplus extraction result of Cremer and McLean (1988) as well as the standard independent private values revenue maximizing auction presented in Myerson (1981), providing a unified treatment for two sets of results irreconcilable so far.