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Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models

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  • David Criens
  • Kathrin Glau
  • Zorana Grbac

Abstract

We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modelling in general. Especially it allows us to carefully discuss the question of well-definedness of semimartingale Libor models, whose construction crucially relies on a sequence of measure changes.

Suggested Citation

  • David Criens & Kathrin Glau & Zorana Grbac, 2017. "Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(1), pages 23-37, January.
    • Handle: RePEc:taf:apmtfi:v:24:y:2017:i:1:p:23-37
    DOI: 10.1080/1350486X.2017.1327324
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    Cited by:

    1. Alessandro Gnoatto & Silvia Lavagnini, 2023. "Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting," Papers 2312.13057, arXiv.org.

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