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Absolutely Continuous Compensators

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, 2011. "Absolutely Continuous Compensators," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 335-351.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:03:n:s0219024911006565
    DOI: 10.1142/S0219024911006565
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    Citations

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    Cited by:

    1. Kokole, Daša & Jané-Llopis, Eva & Mercken, Liesbeth & Natera Rey, Guillermina & Arroyo, Miriam & Pérez Gómez, Augusto & Mejía-Trujillo, Juliana & Piazza, Marina & Bustamante, Ines & O’Donnell, Amy & K, 2023. "Protocol for a process evaluation of SCALA study – Intervention targeting scaling up of primary health care-based prevention and management of heavy drinking and comorbid depression in Latin America," Evaluation and Program Planning, Elsevier, vol. 97(C).
    2. Philip Protter & Alejandra Quintos, 2021. "Stopping Times Occurring Simultaneously," Papers 2111.09458, arXiv.org, revised Nov 2022.
    3. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Jos'e A. Salmer'on & Giulia Di Nunno & Bernardo D'Auria, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," Papers 2208.07163, arXiv.org, revised May 2023.

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