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摘要翻译：
我们建立了一个可违约索赔定价的一般模型。除了通常没有套利假设之外，我们还假设一种违约资产（至少）在违约发生时失去价值。我们证明了在此假设下，在某些标准市场过滤中，违约时间是完全不可达的停止时间；因此，我们开始系统地构造默认时间，特别强调完全不可访问的停止时间。令人惊讶的是，这种抽象的数学结构揭示了一种非常具体和有用的方法，在这种方法中，可以使用市场因素和特质因素来建立违约模型。然后，我们给出了缺省时间的所有相关特征（即Az\'ema上鞅及其Doob-Meyer分解）。我们还提供了可违约索赔价格的显式公式，并分析了在违约事件发生时预期损失在市场上形成的风险溢价。通常的简化框架得到了扩展，以包括可能的经济冲击，特别是在违约时复苏进程的跳跃。这些公式不是经典的，我们指出缺省补偿器或强度过程的知识不再是寻找显式价格的充分量，而是需要Az\'ema上鞅及其Doob-Meyer分解。
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英文标题：
《From the decompositions of a stopping time to risk premium
decompositions》
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作者：
Delia Coculescu
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最新提交年份：
2010
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in some standard market filtrations, default times are totally inaccessible stopping times; we therefore proceed to a systematic construction of default times with particular emphasis on totally inaccessible stopping times. Surprisingly, this abstract mathematical construction, reveals a very specific and useful way in which default models can be built, using both market factors and idiosyncratic factors. We then provide all the relevant characteristics of a default time (i.e. the Az\'ema supermartingale and its Doob-Meyer decomposition) given the information about these factors. We also provide explicit formulas for the prices of defaultable claims and analyze the risk premiums that form in the market in anticipation of losses which occur at the default event. The usual reduced-form framework is extended in order to include possible economic shocks, in particular jumps of the recovery process at the default time. This formulas are not classic and we point out that the knowledge of the default compensator or the intensity process is not anymore a sufficient quantity for finding explicit prices, but we need indeed the Az\'ema supermartingale and its Doob-Meyer decomposition.
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PDF链接：
https://arxiv.org/pdf/0912.4312
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