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On the fundamental theorem of asset pricing with an infinite state space

1991; Elsevier BV; Volume: 20; Issue: 1 Linguagem: Inglês

10.1016/0304-4068(91)90014-k

1873-1538

Kerry Back, Stanley R. Pliska,

Economic theories and models

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.