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Intensity process and compensator: A new filtration expansion approach and the Jeulin--Yor theorem

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  • Xin Guo
  • Yan Zeng
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    Abstract

    Let $(X_t)_{t\ge0}$ be a continuous-time, time-homogeneous strong Markov process with possible jumps and let $\tau$ be its first hitting time of a Borel subset of the state space. Suppose $X$ is sampled at random times and suppose also that $X$ has not hit the Borel set by time $t$. What is the intensity process of $\tau$ based on this information? This question from credit risk encompasses basic mathematical problems concerning the existence of an intensity process and filtration expansions, as well as some conceptual issues for credit risk. By revisiting and extending the famous Jeulin--Yor [Lecture Notes in Math. 649 (1978) 78--97] result regarding compensators under a general filtration expansion framework, a novel computation methodology for the intensity process of a stopping time is proposed. En route, an analogous characterization result for martingales of Jacod and Skorohod [Lecture Notes in Math. 1583 (1994) 21--35] under local jumping filtration is derived.

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    File URL: http://arxiv.org/pdf/0801.3191
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0801.3191.

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    Date of creation: Jan 2008
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    Publication status: Published in Annals of Applied Probability 2008, Vol. 18, No. 1, 120-142
    Handle: RePEc:arx:papers:0801.3191

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    Web page: http://arxiv.org/

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    1. Corrado Benassi & Antonello E. Scorcu, 2003. "Indexation Rules, Risk Aversion and Imperfect Information," Manchester School, University of Manchester, vol. 71(3), pages 330-340, 06.
    2. Xin Guo & Robert A. Jarrow & Yan Zeng, 2009. "Modeling The Recovery Rate In A Reduced Form Model," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 73-97.
    3. Peter Imkeller, 2003. "Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 153-169.
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    Cited by:
    1. Xin Dong & Harry Zheng, 2014. "Intensity Process for a Pure Jump L\'evy Structural Model with Incomplete Information," Papers 1405.3767, arXiv.org.
    2. Beatrice Acciaio & Claudio Fontana & Constantinos Kardaras, 2014. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Papers 1401.7198, arXiv.org, revised Feb 2014.

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