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

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dc.creatorGuo, Xin
dc.creatorZeng, Yan
dc.date2008-01-21
dc.date.accessioned2026-07-07T12:05:37Z
dc.date.available2026-07-07T12:05:37Z
dc.descriptionLet $(X_t)_{t\ge0}$ 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP447 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0801.3191
dc.identifierhttp://arxiv.org/abs/0801.3191
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 1, 120-142
dc.identifierdoi:10.1214/07-AAP447
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208423
dc.subjectProbability
dc.subjectRisk Management
dc.subject60H30, 60G55 (Primary) 60J99 (Secondary)
dc.titleIntensity process and compensator: A new filtration expansion approach and the Jeulin--Yor theorem
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