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A new proof for the conditions of Novikov and Kazamaki

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  • Ruf, Johannes

Abstract

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.

Suggested Citation

  • Ruf, Johannes, 2013. "A new proof for the conditions of Novikov and Kazamaki," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 404-421.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:404-421
    DOI: 10.1016/j.spa.2012.09.011
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    5. 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.
    6. Aleksandar Mijatovi'c & Mikhail Urusov, 2011. "A note on a paper by Wong and Heyde," Papers 1105.3918, arXiv.org.
    7. Daniel Fernholz & Ioannis Karatzas, 2010. "On optimal arbitrage," Papers 1010.4987, arXiv.org.
    8. Hardy Hulley & Eckhard Platen, 2009. "A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales," Research Paper Series 263, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. 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.
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    Citations

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    Cited by:

    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. Hardy Hulley & Johannes Ruf, 2019. "Weak Tail Conditions for Local Martingales," Published Paper Series 2019-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. B. Chikvinidze, 2022. "Necessary and Sufficient Conditions for the Uniform Integrability of the Stochastic Exponential," Journal of Theoretical Probability, Springer, vol. 35(1), pages 282-294, March.
    4. Carole Bernard & Zhenyu Cui & Don McLeish, 2013. "On the martingale property in stochastic volatility models based on time-homogeneous diffusions," Papers 1310.0092, arXiv.org, revised Jul 2014.
    5. Černý, Aleš & Ruf, Johannes, 2023. "Simplified calculus for semimartingales: Multiplicative compensators and changes of measure," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 572-602.
    6. Sascha Desmettre, 2018. "Change of Measure in the Heston Model given a violated Feller Condition," Papers 1809.10955, arXiv.org, revised Oct 2019.

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