ON THE FUNDAMENTAL THEOREM OF ASSET PRICING WITH AN INFINITE STATE-SPACE

An example is given of a securities market in which there is no arbitrage and a risk-neutral agent has an optimal demand subject to a minimum wealth constraint, yet there is no risk-neutral probability measure and no state price density. Also, there is no linear pricing rule on Lp for any p < ∞. This failure of the 'Fundamental Theorem of Asset Pricing' is due to a lack of countable additivity of the pricing operator in the market. Some sufficient conditions are also given for the existence of a risk-neutral probability measure and state price density for pricing L∞ claims. © 1990.