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Strict Local Martingales with Jumps

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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