摘要翻译：
本文针对信用风险中违约时间建模的两个问题给出了一个解决方案。我们首先说明，如果$\tau$是一个任意的随机（默认）时间，使得它的az\'ema的上鞅$z_t^\tau=\p(\tau>t\f_t)$是连续的，那么$\tau$避免停止时间。然后，我们反驳了第一次出现在{jenbrutk1}中的一个关于危险过程与鞅危险过程相等的猜想，并证明了如何将其修改为定理。在\cite{AshkanYor}中引入的伪停止时间是这两个过程相等的随机时间的最一般类别。我们还表明，当$\tau$是一个诚实的时间时，这两个过程总是不同的。
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英文标题：
《Hazard processes and martingale hazard processes》
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作者：
Delia Coculescu and Ashkan Nikeghbali
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最新提交年份：
2008
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分类信息：

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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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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英文摘要：
  In this paper, we provide a solution to two problems which have been open in default time modeling in credit risk. We first show that if $\tau$ is an arbitrary random (default) time such that its Az\'ema's supermartingale $Z_t^\tau=\P(\tau>t|\F_t)$ is continuous, then $\tau$ avoids stopping times. We then disprove a conjecture about the equality between the hazard process and the martingale hazard process, which first appeared in \cite{jenbrutk1}, and we show how it should be modified to become a theorem. The pseudo-stopping times, introduced in \cite{AshkanYor}, appear as the most general class of random times for which these two processes are equal. We also show that these two processes always differ when $\tau$ is an honest time.
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PDF链接：
https://arxiv.org/pdf/0807.4958