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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.

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, October.
    • Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:343-348
    DOI: 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. Zühlsdorff, Christian, 2002. "The Pricing of Derivatives on Assets with Quadratic Volatility," Bonn Econ Discussion Papers 5/2002, University of Bonn, Bonn Graduate School of Economics (BGSE).
    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. repec:uts:finphd:40 is not listed on IDEAS
    5. repec:dau:papers:123456789/5374 is not listed on IDEAS
    6. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292, July.
    7. 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.
    8. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkiö, 2023. "Optional projection under equivalent local martingale measures," Finance and Stochastics, Springer, vol. 27(2), pages 435-465, April.
    9. 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.
    10. Salvador Cruz Rambaud, 2019. "Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    11. Matteo Burzoni & Marco Frittelli & Zhaoxu Hou & Marco Maggis & Jan Obłój, 2019. "Pointwise Arbitrage Pricing Theory in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1034-1057, August.
    12. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkio, 2020. "Optional projection under equivalent local martingale measures," Papers 2003.09940, arXiv.org.
    13. Xing Jin & Xudong Zeng, 2018. "Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 347-376, May.
    14. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    15. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    16. Christian Zuhlsdorff, 2001. "The pricing of derivatives on assets with quadratic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 235-262.
    17. Christian Bender, 2012. "Simple arbitrage," Papers 1210.5391, arXiv.org.
    18. 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.
    19. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    20. 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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