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A new proof for the conditions of Novikov and Kazamaki

  • Ruf, Johannes
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    This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the existence of Föllmer’s measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912002128
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 404-421

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:404-421
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    1. 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.
    2. Blei, Stefan & Engelbert, Hans-Jürgen, 2009. "On exponential local martingales associated with strong Markov continuous local martingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2859-2880, September.
    3. 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.
    4. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    5. Aleksandar Mijatovi\'c & Mikhail Urusov, 2011. "A note on a paper by Wong and Heyde," Papers 1105.3918, arXiv.org.
    6. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    7. Mayerhofer, Eberhard & Muhle-Karbe, Johannes & Smirnov, Alexander G., 2011. "A characterization of the martingale property of exponentially affine processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 568-582, March.
    8. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
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