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

• 成果类型: Article
• 署名作者: Guo, Xin; Zeng, Yan
• 署名单位: University of California System; University of California Berkeley; Bloomberg L.P.
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP447
• 发表日期: 2008
• 页码: 120-142
• 关键词: additional logarithmic utility; Credit risk; INFORMATION; INSIDERS; default; models

摘要

Let (X-t)(t >= 0) 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.