The valuation problem in arbitrage price theory
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 not there exists a continuous, strictly positive, linear extension \(P\) of \(p\) from \(M\) to the entire contingent claims space \(X\). This problem has a relatively simple solution for a large family of financial models, including those for which \(X\) is a separable Banach space or \(X\) is a classical Banach lattice. Indeed, the linear extension \(P\) exists if and only if a condition closely related to Kreps' axiom of no free lunches is satisfied. In addition, a hierarchy of no arbitrage axioms is proposed and analyzed, and the connection with DeFinetti's theory of subjective probability is illuminated.
scientific article; zbMATH DE number 458840
scientific article