= Incomplete market
A market is incomplete if some <contingent claim> cannot be replicated by a <self-financing strategy>. In a one-period finite-state market, attainable payoff vectors form the span of the traded assets' terminal payoff vectors. If this span is a proper subspace of the full payoff space, the market is incomplete. For example, two linearly independent asset-payoff vectors on three states leave at least one payoff direction unattainable. Absence of <arbitrage> only requires an appropriate positive <state-price density>; it does not imply that every claim is attainable.
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