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摘要翻译：
设$(X_t)_{t\ge0}$是一个连续时间的、时间齐次的具有可能跳跃的强Markov过程，设$\tau$是它在状态空间的Borel子集的首次命中时间。假设$x$是随机采样的，并且还假设$x$没有达到由时间$t$设置的Borel。基于此信息的$\tau$强度过程是什么？这个来自信用风险的问题包括关于强度过程和过滤扩张的存在性的基本数学问题，以及信用风险的一些概念问题。通过对Jeulin-Yor[MATH课堂讲稿649(1978)78-97]关于补偿器的著名结果的回顾和推广，提出了一种新的计算停止时间强度过程的方法。在此过程中，我们得到了Jacod和Skorohod鞅在局部跳跃过滤下的类似刻画结果[Math课堂讲稿1583(1994)21--35]。
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英文标题：
《Intensity process and compensator: A new filtration expansion approach
and the Jeulin--Yor theorem》
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作者：
Xin Guo, Yan Zeng
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0801.3191
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