Please use this identifier to cite or link to this item: https://doi.org/10.1006/jeth.2000.2737
Title: Asymptotic arbitrage and the APT with or without measure-theoretic structures
Authors: Khan, M.A.
Sun, Y. 
Keywords: Arbitrage pricing theory
Asymptotic arbitrage
Continuity of cost functionals
Factor structure
Finitely-additive measure space
Lebesgue continuum
Reisz representation theorem
Issue Date: 2001
Source: Khan, M.A., Sun, Y. (2001). Asymptotic arbitrage and the APT with or without measure-theoretic structures. Journal of Economic Theory 101 (1) : 222-251. ScholarBank@NUS Repository. https://doi.org/10.1006/jeth.2000.2737
Abstract: We present a version of the APT based on an asset index set of an arbitrary infinite cardinality. Under assumptions due to Ross (1976, J. Econ. Theory 13, 341-360) and Chamberlain and Rothschild (1983, Econometrica 51, 1281-1303), we show 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. Journal of Economic Literature Classification Numbers: G12, C60. © 2001 Academic Press.
Source Title: Journal of Economic Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/102886
ISSN: 00220531
DOI: 10.1006/jeth.2000.2737
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