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Intensity process and compensator: A new filtration expansion approach and the Jeulin–Yor theorem. The Annals of Applied Probability (2007)
| Citations: | 16 - 2 self |
BibTeX
@MISC{Guo07intensityprocess,
author = {Guo and Yan Zeng},
title = {Intensity process and compensator: A new filtration expansion approach and the Jeulin–Yor theorem. The Annals of Applied Probability},
year = {2007}
}
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Abstract
Let (Xt)t≥0 be a continuous-time, time-homogeneous strong Markov process with possible jumps and let τ 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 τ 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.
Keyphrases
intensity process jeulin yor theorem new filtration expansion approach applied probability credit risk filtration expansion first hitting time stopping time novel computation methodology general filtration expansion framework conceptual issue borel subset skorohod lecture note basic mathematical problem analogous characterization result possible jump state space time-homogeneous strong markov process local jumping filtration en route random time famous jeulin yor lecture note
