The valuation problem in arbitrage price theory

Abstract Suppose a continuous, strictly positive, linear price functional p is given on a subspace M of marketed claims. The valuation problem consists of verifying whether or notthere exists a continuous, strictly positive, linear extension of p from M to the entire contingent claims space X . We solve this problem when X belongs to a large class of Banach lattices including the classical Banach spaces, and also simplify some analogous results found in the literature for other types of financial models.

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