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# The Second Fundamental Theorem of Asset Pricing: An arbitrage-free market ( S, B ) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a unique risk-neutral measure that is equivalent to P and has numeraire B.
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# The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space ( Ω,, ) is arbitrage-free if and only if there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
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