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Simple examples of pure-jump strict local martingales

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  • Martin Keller-Ressel

Abstract

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equation. Finally we show an alternative construction for our examples by an absolutely continuous measure change in the spirit of (Delbaen and Schachermayer, PTRF 1995).

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  • Martin Keller-Ressel, 2014. "Simple examples of pure-jump strict local martingales," Papers 1405.2669, arXiv.org, revised Jun 2015.
    • Handle: RePEc:arx:papers:1405.2669
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    References listed on IDEAS

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    1. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
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    3. Philip Protter, 2013. "Strict Local Martingales with Jumps," Papers 1307.2436, arXiv.org, revised Mar 2014.
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    Cited by:

    1. 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.
    2. Philip Protter & Aditi Dandapani, 2019. "Strict Local Martingales and the Khasminskii test for Explosions," Papers 1903.02383, arXiv.org.
    3. Protter, Philip, 2015. "Strict local martingales with jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1352-1367.

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