违约后会发生什么：条件密度方法
What happens after a default: the conditional density approach
摘要：
我们提出了一个一般模型的默认时间，精确的强度过程的作用，并表明，这个过程允许的知识的条件分布的默认只有“之前的默认”。在多默认设置中工作时，这种信息的缺乏是至关重要的。在一个单一的违约情况下，强度过程的知识不允许计算违约索赔的价格，除非在浸入性质得到满足的情况下。在本文中，我们提出了密度方法的违约时间。密度过程将给出默认时间和参考过滤之间的联系的充分表征，特别是“默认时间之后”。我们还研究了完全滤子中的鞅用参考滤子中的鞅来描述，以及Girsanov变换对密度过程、强度过程以及浸入性质的影响.
英文摘要：
We present a general model for default time, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of information is crucial while working in a multi-default setting. In a single default case, the knowledge of the intensity process does not allow to compute the price of defaultable claims, except in the case where immersion property is satisfied. We propose in this paper the density approach for default time. The density process will give a full characterization of the links between the default time and the reference filtration, in particular "after the default time". We also investigate the description of martingales in the full filtration in terms of martingales in the reference filtration, and the impact of Girsanov transformation on the density and intensity processes, and also on the immersion property.
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