IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1307.2436.html
   My bibliography  Save this paper

Strict Local Martingales with Jumps

Author

Listed:
  • Philip Protter

Abstract

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a phenomenon we would contend is common in applications such as filtering, control, and especially in mathematical finance. We give a method for constructing such examples and analyze one particular method in detail.

Suggested Citation

  • Philip Protter, 2013. "Strict Local Martingales with Jumps," Papers 1307.2436, arXiv.org, revised Mar 2014.
    • Handle: RePEc:arx:papers:1307.2436
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1307.2436
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    2. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    3. Claudio Fontana & Monique Jeanblanc & Shiqi Song, 2012. "On arbitrages arising from honest times," Papers 1207.1759, arXiv.org, revised Jul 2013.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Johannes Ruf & Wolfgang Runggaldier, 2013. "A Systematic Approach to Constructing Market Models With Arbitrage," Papers 1309.1988, arXiv.org, revised Dec 2013.
    2. Martin Keller-Ressel, 2014. "Simple examples of pure-jump strict local martingales," Papers 1405.2669, arXiv.org, revised Jun 2015.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    2. Aditi Dandapani & Philip Protter, 2019. "Strict Local Martingales Via Filtration Enlargement," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-28, December.
    3. David Criens, 2016. "Deterministic Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets," Papers 1609.01621, arXiv.org, revised Dec 2017.
    4. Francesca Biagini & Hans Föllmer & Sorin Nedelcu, 2014. "Shifting martingale measures and the birth of a bubble as a submartingale," Finance and Stochastics, Springer, vol. 18(2), pages 297-326, April.
    5. Roseline Bilina Falafala & Robert A. Jarrow & Philip Protter, 2016. "Relative asset price bubbles," Annals of Finance, Springer, vol. 12(2), pages 135-160, May.
    6. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, April.
    7. Sergio Pulido, 2010. "The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions," Papers 1012.3102, arXiv.org, revised Jan 2014.
    8. Paolo Guasoni & Miklós Rásonyi, 2015. "Fragility of arbitrage and bubbles in local martingale diffusion models," Finance and Stochastics, Springer, vol. 19(2), pages 215-231, April.
    9. Protter, Philip, 2015. "Strict local martingales with jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1352-1367.
    10. David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    11. Travis Fisher & Sergio Pulido & Johannes Ruf, 2015. "Financial Models with Defaultable Num\'eraires," Papers 1511.04314, arXiv.org, revised Oct 2017.
    12. Travis Fisher & Sergio Pulido & Johannes Ruf, 2017. "Financial Models with Defaultable Numéraires," Working Papers hal-01240736, HAL.
    13. Wong, Bernard, 2009. "Explicit construction of stochastic exponentials with arbitrary expectation k[set membership, variant](0,1)," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 880-883, April.
    14. Robert A. Jarrow & Simon S. Kwok, 2021. "Inferring financial bubbles from option data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 1013-1046, November.
    15. repec:uts:finphd:40 is not listed on IDEAS
    16. Li, Xue-Mei, 2017. "Strict local martingales: Examples," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 65-68.
    17. Kasper Larsen & Hang Yu, 2012. "Horizon dependence of utility optimizers in incomplete models," Finance and Stochastics, Springer, vol. 16(4), pages 779-801, October.
    18. Claudio Fontana, 2015. "Weak And Strong No-Arbitrage Conditions For Continuous Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-34.
    19. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2010. "Valuation equations for stochastic volatility models," Papers 1004.3299, arXiv.org, revised Dec 2011.
    20. 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.
    21. Gianluca Cassese, 2017. "Asset pricing in an imperfect world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 539-570, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1307.2436. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.