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A note on the existence of unique equivalent martingale measures in a Markovian setting

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  • Tina Hviid Rydberg

    ()
    (University of Aarhus, Department of Theoretical Statistics, Ny Munkegade Bldg. 530, DK-8000 århus C, Denmark)

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    Abstract

    Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to problems in mathematical finance. Two examples of models for which the question of existence was unresolved are studied. By means of our results existence of a unique equivalent measure up to an explosion time is proved.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 1 (1997)
    Issue (Month): 3 ()
    Pages: 251-257

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    Handle: RePEc:spr:finsto:v:1:y:1997:i:3:p:251-257

    Note: received: May 1996; final version received: March 1997
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Explosion time; hyperbolic diffusion processes; normal inverse Gaussian diffusion processes; stochastic differential equations; unique solution in law;

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    Cited by:
    1. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "A Mean-Reverting SDE on Correlation matrices," Post-Print hal-00617111, HAL.
    2. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    3. Barndorff-Nielsen, Ole E. & Pérez-Abreu, Victor, 1999. "Stationary and self-similar processes driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 357-369, December.
    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    5. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1472-1520.
    6. 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.

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