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Absolutely Continuous Compensators

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Author Info

  • SVANTE JANSON

    ()
    (Uppsala University, Department of Mathematics, P. O. Box 480, SE-751 06 Uppsala, Sweden)

  • SOKHNA M'BAYE

    ()
    (Département de de Mathématiques, École Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France)

  • PHILIP PROTTER

    ()
    (Statistics Department, Columbia University, New York, NY 10027, USA)

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    Abstract

    We give sufficient conditions on the underlying filtration such that all totally inaccessible stopping times have compensators which are absolutely continuous. If a semimartingale, strong Markov process X has a representation as a solution of a stochastic differential equation driven by a Wiener process, Lebesgue measure, and a Poisson random measure, then all compensators of totally inaccessible stopping times are absolutely continuous with respect to the minimal filtration generated by X. However Çinlar and Jacod have shown that all semimartingale strong Markov processes, up to a change of time and slightly of space, have such a representation.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 03 ()
    Pages: 335-351

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:03:p:335-351

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    Related research

    Keywords: Compensator; dual predictable projection; Doob-Meyer decomposition; credit risk; martingale; hazard rate;

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    Cited by:
    1. Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Science & Finance (CFM) working paper archive 1403.5402, Science & Finance, Capital Fund Management.
    2. Çetin, Umut, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3619-3647.

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