Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures
AbstractWe present a version of the APT based on an asset index set of an arbitrary infinite cardinality. Under assumptions due to Ross and Chamberlain-Rothschild, we shhow that in the absence of gains from asymptotic arbitrage, the square of the deviations of the individual rates of return from a factor-pricing formula sum to a finite number ; and that this absence, while sufficient, is not necessary for the formula to hold. We relate these results to recent work, and explain, in particular, how a version of the APT exhibits several inconsistencies when the index set is the Lebesgue unit interval.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 101 (2001)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/locate/inca/622869
Other versions of this item:
- Khan, A. & Sun, Y., 2000. "Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures," Papiers d'Economie MathÃÂ©matique et Applications 2000.81, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
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