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Diversity and arbitrage in a regulatory breakup model


  • Winslow Strong


  • Jean-Pierre Fouque



In 1999 Robert Fernholz observed an inconsistency between the normative assumption of existence of an equivalent martingale measure (EMM) and the empirical reality of diversity in equity markets. We explore a method of imposing diversity on market models by a type of antitrust regulation that is compatible with EMMs. The regulatory procedure breaks up companies that become too large, while holding the total number of companies constant by imposing a simultaneous merge of other companies. The regulatory events are assumed to have no impact on portfolio values. As an example, regulation is imposed on a market model in which diversity is maintained via a log-pole in the drift of the largest company. The result is the removal of arbitrage opportunities from this market while maintaining the market's diversity.
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Suggested Citation

  • Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
  • Handle: RePEc:kap:annfin:v:7:y:2011:i:3:p:349-374
    DOI: 10.1007/s10436-010-0175-1

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    References listed on IDEAS

    1. Adrian Banner & Daniel Fernholz, 2008. "Short-term relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 4(4), pages 445-454, October.
    2. Robert A. Jarrow, 2015. "Asset Price Bubbles," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 201-218, December.
    3. Fernholz, Robert, 1999. "On the diversity of equity markets," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 393-417, April.
    4. Jörg Osterrieder & Thorsten Rheinländer, 2006. "Arbitrage Opportunities in Diverse Markets via a Non-equivalent Measure Change," Annals of Finance, Springer, vol. 2(3), pages 287-301, July.
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    Cited by:

    1. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-Weighted Portfolios with Negative Parameter," Papers 1504.01026,, revised Jul 2015.
    2. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877,, revised Oct 2013.
    3. Andrey Sarantsev, 2014. "On a class of diverse market models," Annals of Finance, Springer, vol. 10(2), pages 291-314, May.
    4. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988,
    5. Winslow Strong, 2011. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Papers 1112.5340,
    6. Alexander Vervuurt & Ioannis Karatzas, 2015. "Diversity-weighted portfolios with negative parameter," Annals of Finance, Springer, vol. 11(3), pages 411-432, November.
    7. Winslow Strong, 2014. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Finance and Stochastics, Springer, vol. 18(3), pages 487-514, July.

    More about this item


    Diversity; Arbitrage; Relative arbitrage; Equivalent martingale measure; Antitrust; Regulation; G11;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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