Problems of Equilibria in Insurance Markets with Asymmetric Information

Equilibrium has been a central notion in economics, since before the seminal work of Léon Walras [1926]. Therefore, it was a great step forward when Kenneth J. Arrow [1953] and Gérard Debreu [1953] simultaneously developed the concept of “equilibrium under uncertainty” (see also the alternative approach of Maurice Allais [1953]). By introducing “contingent commodities” or “contingent claims” they generalized the results of the classical theory of general equilibrium to the case of an uncertain (stochastic) environment. With this ingenious device Arrow and Debreu were able to show that a competitive equilibrium is a Pareto-optimal allocation also under uncertainty: There is a price for every state of nature or event; the prices are determined by the “unpersonal forces of the market” and are beyond the individual agent’s control. This equilibrium price set supports a distribution of consumption (or income) claims that is Pareto-optimal in terms of expected utility. But this result is obtained at a relatively high cost: The prices of contingent claims or Arrow-certificates depend on the probability distribution of events, the total amount to be transacted in a specific state or event, and the agents’ marginal utility of income: “In order to reach the result, we have to introduce an infinity—in the geneal case a continuum—of commodities and prices” (Borch [1968], p. 256), as well as an infinity of markets for every commodity in every state or event.