Asymptotic arbitrage and the APT with or without measure-theoretic structures

• 成果类型: Article
• 署名作者: Khan, MA; Sun, YN
• 署名单位: Johns Hopkins University; National University of Singapore
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2000.2737
• 发表日期: 2001
• 页码: 222-251
• 关键词: arbitrage pricing theory; asymptotic arbitrage; continuity of cost functionals; Reisz representation theorem; factor structure; finitely-additive measure space; Lebesgue continuum

摘要

We present a version of the APT based on an asset index set of all 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. (C) 2001 Academic Press.