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Arbitrage And Free Lunch With Bounded Risk For Unbounded Continuous Processes

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  • Freddy Delbaen
  • Walter Schachermayer

Abstract

We give two examples showing that for unbounded continuous price processes, the no-free-lunch assumption and the existence of an equivalent martingale measure are not equivalent. In fact it turns out that the notion of an equivalent local martingale measure is natural in this context. Copyright 1994 Blackwell Publishers.

Suggested Citation

  • Freddy Delbaen & Walter Schachermayer, 1994. "Arbitrage And Free Lunch With Bounded Risk For Unbounded Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 343-348.
  • Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:343-348
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1994.tb00063.x
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    Citations

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    Cited by:

    1. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org, revised Jun 2015.
    2. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    3. Erhan Bayraktar & Hasanjan Sayit, 2010. "No arbitrage conditions for simple trading strategies," Annals of Finance, Springer, vol. 6(1), pages 147-156, January.
    4. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292.
    5. Christian Zühlsdorff, 2002. "The Pricing of Derivatives on Assets with Quadratic Volatility," Bonn Econ Discussion Papers bgse5_2002, University of Bonn, Germany.
    6. repec:dau:papers:123456789/5374 is not listed on IDEAS
    7. Alexander M. G. Cox & Zhaoxu Hou & Jan Obłój, 2016. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Finance and Stochastics, Springer, vol. 20(3), pages 669-704, July.
    8. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    9. Matteo Burzoni & Marco Frittelli & Zhaoxu Hou & Marco Maggis & Jan Ob{l}'oj, 2016. "Pointwise Arbitrage Pricing Theory in Discrete Time," Papers 1612.07618, arXiv.org, revised Feb 2018.
    10. Christian Zuhlsdorff, 2001. "The pricing of derivatives on assets with quadratic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 235-262.
    11. Christian Bender, 2012. "Simple arbitrage," Papers 1210.5391, arXiv.org.
    12. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    13. Roseline Bilina Falafala & Robert A. Jarrow & Philip Protter, 2016. "Relative asset price bubbles," Annals of Finance, Springer, vol. 12(2), pages 135-160, May.

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