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Diversity and no arbitrage

Author

Listed:
  • Attila Herczegh
  • Vilmos Prokaj
  • Mikl'os R'asonyi

Abstract

A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can one tell whether an observed diverse market admits arbitrage? In the present paper we argue that this may well be impossible by proving that the known examples of diverse markets in the literature (which do admit arbitrage) can be approximated uniformly (on the logarithmic scale) by models which are both diverse and arbitrage-free.

Suggested Citation

  • Attila Herczegh & Vilmos Prokaj & Mikl'os R'asonyi, 2013. "Diversity and no arbitrage," Papers 1301.4173, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1301.4173
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    References listed on IDEAS

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    1. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    2. 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.
    3. Fernholz, Robert, 1999. "On the diversity of equity markets," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 393-417, April.
    4. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    5. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
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    Cited by:

    1. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    2. Takaki Hayashi & Yuta Koike, 2017. "No arbitrage and lead-lag relationships," Papers 1712.09854, arXiv.org.
    3. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," CREATES Research Papers 2013-38, Department of Economics and Business Economics, Aarhus University.
    4. Czichowsky, Christoph & Schachermayer, Walter, 2017. "Portfolio optimisation beyond semimartingales: shadowprices and fractional Brownian motion," LSE Research Online Documents on Economics 67689, London School of Economics and Political Science, LSE Library.
    5. Mikl'os R'asonyi & Hasanjan Sayit, 2015. "Sticky processes, local and true martingales," Papers 1509.08280, arXiv.org, revised Mar 2017.
    6. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," Papers 1310.7857, arXiv.org, revised Aug 2014.

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