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Diversity and relative arbitrage in equity markets

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Author Info

  • Robert Fernholz

    ()

  • Ioannis Karatzas

    ()

  • Constantinos Kardaras

    ()

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    Abstract

    An equity market is called “diverse” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “weak diversity” and “asymptotic weak diversity”) in precise terms. We show that diversity is possible to achieve, but delicate. Several examples are provided which illustrate these notions and show that weakly-diverse markets contain relative arbitrage opportunities: it is possible to outperform or underperform such markets over any given time-horizon. The existence of this type of relative arbitrage does not interfere with the development of contingent claim valuation, and has consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study. Copyright Springer-Verlag Berlin/Heidelberg 2005

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 9 (2005)
    Issue (Month): 1 (January)
    Pages: 1-27

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    Handle: RePEc:spr:finsto:v:9:y:2005:i:1:p:1-27

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Financial markets; portfolios; diversity; relative arbitrage; order statistics; local times; stochastic differential equations; strict local martingales;

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    Citations

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    Cited by:
    1. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2012. "Strict local martingale deflators and valuing American call-type options," Finance and Stochastics, Springer, vol. 16(2), pages 275-291, April.
    2. Soumik Pal & Ting-Kam Leonard Wong, 2013. "Energy, entropy, and arbitrage," Papers 1308.5376, arXiv.org.
    3. Kardaras, Constantinos & Platen, Eckhard, 2011. "On the semimartingale property of discounted asset-price processes," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2678-2691, November.
    4. Ioannis Karatzas & Constantinos Kardaras, 2008. "The numeraire portfolio in semimartingale financial models," Papers 0803.1877, arXiv.org.
    5. Aleksandar Mijatović & Mikhail Urusov, 2012. "Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models," Finance and Stochastics, Springer, vol. 16(2), pages 225-247, April.
    6. Constantinos Kardaras, 2008. "Balance, growth and diversity of financial markets," Annals of Finance, Springer, vol. 4(3), pages 369-397, July.
    7. Eckhard Platen & Renata Rendek, 2010. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 282, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. 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.
    9. 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.
    10. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    11. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877, arXiv.org, revised Oct 2013.
    12. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
    13. Soumik Pal & Ting-Kam Leonard Wong, 2014. "The geometry of relative arbitrage," Papers 1402.3720, arXiv.org, revised Mar 2014.
    14. Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.
    15. Adrian D. Banner & Robert Fernholz & Ioannis Karatzas, 2006. "Atlas models of equity markets," Papers math/0602521, arXiv.org.
    16. Andrey Sarantsev, 2014. "On a class of diverse market models," Annals of Finance, Springer, vol. 10(2), pages 291-314, May.
    17. Attila Herczegh & Vilmos Prokaj & Mikl\'os R\'asonyi, 2013. "Diversity and no arbitrage," Papers 1301.4173, arXiv.org.
    18. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.

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