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Absolutely Continuous Compensators

In: Finance at Fields

Author

Listed:
  • 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)

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.

Suggested Citation

  • Svante Janson & Sokhna M'Baye & Philip Protter, 2012. "Absolutely Continuous Compensators," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 19, pages 433-449, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407892_0019
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