The valuation problem in arbitrage price theory
type: Item
instance of: scholarly article
title: The valuation problem in arbitrage price theory
zbMATH Open document ID: 0793.90008
DOI: 10.1016/0304-4068(93)90037-L
author: Stephen A. Clark
published in: Journal of Mathematical Economics
publication date: 1994-08-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B24
zbMATH DE Number: 458840
zbMATH Keywords: marketed claims
zbMATH Keywords: linear extension
zbMATH Keywords: hierarchy of no arbitrage axioms
zbMATH Keywords: subjective probability
MaRDI profile type: Publication
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full work available at URL: 0304-4068(93)90037-l
OpenAlex ID: W2092752383
description: scientific article; zbMATH DE number 458840