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A Market Test for the Positivity of Arrow-Debreu Prices
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We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to show that this no arbitrage condition is equivalent to the positive semidefiniteness of matrices formed by the market price of tradeable securities and their products. We apply this result to a market with multiple assets and basket call options.
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