Incomplete market

In economics, incomplete markets are markets in which the number of Arrow–Debreu securities is less than the number of states of nature. In contrast with complete markets, this shortage of securities will likely restrict individuals from transferring the desired level of wealth among states.

An Arrow security purchased or sold at date t is a contract promising to deliver one unit of income in one of the possible contingencies which can occur at date t + 1. If at each date-event there exists a complete set of such contracts, one for each contingency that can occur at the following date, individuals will trade these contracts in order to insure against future risks, targeting a desirable and budget feasible level of consumption in each state (i.e. consumption smoothing). In most set ups when these contracts are not available, optimal risk sharing between agents will not be possible. For this scenario, agents (homeowners, workers, firms, investors, etc.) will lack the instruments to insure against future risks such as employment status, health, labor income, prices, among others.

In a competitive market, each agent makes intertemporal choices in a environment. Their attitudes toward risk, the production possibility set, and the set of available trades determine the equilibrium quantities and prices of assets that are traded. In an "idealized" representation agents are assumed to have costless contractual enforcement and perfect knowledge of future states and their likelihood. With a complete set of state contingent claims (also known as Arrow–Debreu securities) agents can trade these securities to hedge against undesirable or bad outcomes.

When a market is incomplete, it typically fails to make the optimal allocation of assets. That is, the First Welfare Theorem no longer holds. The competitive equilibrium in an Incomplete Market is generally constrained suboptimal. The notion of constrained suboptimality was formalized by Geanakoplos and Polemarchakis (1986).

Despite the latest ongoing innovation in financial and insurance markets, markets remain incomplete. While several contingent claims are traded routinely against many states such as insurance policies, futures, financial options, among others, the set of outcomes is far greater than the set of claims.

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