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Strict local martingales: Examples

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  • Li, Xue-Mei

Abstract

We show that a continuous local martingale is a strict local martingale if its supremum process is not in Lα for a positive number α smaller than 1. Using this we construct a family of strict local martingales.

Suggested Citation

  • Li, Xue-Mei, 2017. "Strict local martingales: Examples," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 65-68.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:65-68
    DOI: 10.1016/j.spl.2017.04.025
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    References listed on IDEAS

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    1. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    2. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
    3. Hardy Hulley & Eckhard Platen, 2009. "A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales," Research Paper Series 263, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    5. Loewenstein, Mark & Willard, Gregory A., 2000. "Rational Equilibrium Asset-Pricing Bubbles in Continuous Trading Models," Journal of Economic Theory, Elsevier, vol. 91(1), pages 17-58, March.
    6. 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.
    7. Protter, Philip, 2015. "Strict local martingales with jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1352-1367.
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    Cited by:

    1. Robert Jarrow & Philip Protter, 2020. "Credit Risk, Liquidity, and Bubbles," International Review of Finance, International Review of Finance Ltd., vol. 20(3), pages 737-746, September.
    2. Philip Protter & Aditi Dandapani, 2019. "Strict Local Martingales and the Khasminskii test for Explosions," Papers 1903.02383, arXiv.org.
    3. Dandapani, Aditi & Protter, Philip, 2022. "Strict local martingales and the Khasminskii test for explosions," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 716-728.

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