英文标题：
《BSDEs with default jump》
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作者：
Roxana Dumitrescu, Marie-Claire Quenez and Agn\\`es Sulem
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最新提交年份：
2017
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英文摘要：
We study the properties of nonlinear Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale measure associated with a default jump with intensity process $(\\lambda_t)$. We give a priori estimates for these equations and prove comparison and strict comparison theorems. These results are generalized to drivers involving a singular process. The special case of a $\\lambda$-linear driver is studied, leading to a representation of the solution of the associated BSDE in terms of a conditional expectation and an adjoint exponential semi-martingale. We then apply these results to nonlinear pricing of European contingent claims in an imperfect financial market with a totally defaultable risky asset. The case of claims paying dividends is also studied via a singular process.
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中文摘要：
研究了由布朗运动和鞅测度驱动的非线性倒向随机微分方程（BSDE）的性质。我们给出了这些方程的先验估计，并证明了比较定理和严格比较定理。这些结果推广到涉及奇异过程的驱动因素。研究了$\\λ$-线性驱动的特例，给出了相关BSDE解的条件期望和伴随指数半鞅表示。然后，我们将这些结果应用于具有完全违约风险资产的不完善金融市场中欧洲未定权益的非线性定价。还通过奇异过程研究了支付股息的债权的情况。
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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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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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