摘要翻译：
本文主要研究具有随机终端时间的BSDE的存在唯一性的数学问题，它是一个一般的随机变量，而不是以往文献中关于具有随机终端时间的BSDE的一般情况。这项工作的主要动机是一个金融或精算问题的套期未偿或未定索赔或人寿保险合同，其结束时间是一个违约时间或死亡时间，而不是停止时间。我们必须对布朗过滤进行逐步放大，并在这种放大的过滤下求解得到的BSDE。本文给出了这一数学问题的解，并在一定的一般条件下证明了这类BSDE解的存在唯一性。将该方法应用于可违约未定权益的套期保值金融问题，给出了可违约未定权益或寿险合同的套期保值策略的表达式。
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英文标题：
《Hedging of Defaultable Contingent Claims using BSDE with uncertain time
  horizon》
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作者：
Christophette Blanchet-Scalliet (ICJ), Anne Eyraud-Loisel (SAF),
  Manuela Royer-Carenzi (LATP)
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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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：
  This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or actuarial problem of hedging of defaultable contingent claims or life insurance contracts, for which the terminal time is a default time or a death time, which are not stopping times. We have to use progressive enlargement of the Brownian filtration, and to solve the obtained BSDE under this enlarged filtration. This work gives a solution to the mathematical problem and proves the existence and uniqueness of solutions of such BSDE under certain general conditions. This approach is applied to the financial problem of hedging of defaultable contingent claims, and an expression of the hedging strategy is given for a defaultable contingent claim or a life insurance contract.
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PDF链接：
https://arxiv.org/pdf/0811.4039