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We examine insurance markets with two types of customers: those who regret suboptimal decisions and those who don.t. In this setting, we characterize the equilibria under hidden information about the type of customers and hidden action. We show that both pooling and separating equilibria can exist. Furthermore, there exist separating equilibria that predict a positive correlation between the amount of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the amount of insurance coverage and risk type, i.e. advantageous selection. Since optimal choice of regretful customers depends on foregone alternatives, any equilibrium includes a contract which is o¤ered but not purchased.
When a spot market monopolist participates in a derivatives market, she has an incentive to deviate from the spot market monopoly optimum to make her derivatives market position more profitable. When contracts can only be written contingent on the spot price, a risk-averse monopolist chooses to participate in the derivatives market to hedge her risk, and she reduces expected profits by doing so. However, eliminating all risk is impossible. These results are independent of the shape of the demand function, the distribution of demand shocks, the nature of preferences or the set of derivatives contracts.