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Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures

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  • Khan, A.
  • Sun, Y.

Abstract

We 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.

Suggested Citation

  • Khan, A. & Sun, Y., 2000. "Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures," Papiers d'Economie Mathématique et Applications 2000.81, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:fth:pariem:2000.81
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    References listed on IDEAS

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    10. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 541-560.
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    Cited by:

    1. Birge, John R. & Yang, Song, 2007. "A model for tax advantages of portfolios with many assets," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3269-3290, November.
    2. Herzberg, Frederik, 2011. "On the foundations of Lévy finance. Equilibrium for a single-agent financial market with jumps," Center for Mathematical Economics Working Papers 406, Center for Mathematical Economics, Bielefeld University.
    3. Laurence Carassus & Miklos Rasonyi, 2019. "Risk-neutral pricing for APT," Papers 1904.11252, arXiv.org, revised Oct 2020.
    4. Anderson, Robert M. & Raimondo, Roberto C., 2007. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Department of Economics, Working Paper Series qt0zq6v5gd, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    5. Khan, M. Ali & Sun, Yeneng, 2003. "Exact arbitrage, well-diversified portfolios and asset pricing in large markets," Journal of Economic Theory, Elsevier, vol. 110(2), pages 337-373, June.
    6. Michailidis, G., 2009. "Multivariate methods in examining macroeconomic variables effect on Greek stock market returns, 1997-2004," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    7. M. Ali Khan & Yeneng Sun, 2003. "Exact arbitrage and portfolio analysis in large asset markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 495-528, October.
    8. Kim Sawyer & André Gygax & Matthew Hazledine, 2010. "Pricing errors and estimates of risk premia in factor models," Annals of Finance, Springer, vol. 6(3), pages 391-403, July.

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    More about this item

    Keywords

    ARBITRAGE ; PRICING ; COSTS;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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