On the fundamental theorem of asset pricing with an infinite state space
An example is given of a securities market in which there are no arbitrage opportunities - moreover, a risk-neutral agent facing a nonnegative wealth constraint has an optimal trading strategy - yet there is no equivalent martingale measure and no state price density. This failure of the ``Fundamental Theorem of Asset Pricing'' is due to the fact that the pricing operator for \(L^{\infty}\) claims is not countably additive - it is a finitely additive measure with a nontrivial purely finitely additive component. Some new sufficient conditions are given for this measure to be countably additive.
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