摘要翻译：
本文在由连续局部鞅生成的随机基础上，考虑了一类具有二次增长驱动的BSDEs。首先，当生成鞅是强马尔可夫过程时，我们得到了向前-向后系统(FBSDE)的马尔可夫性质。然后我们建立了FBSDE关于其前向分量初值的可微性。这使我们得到了本文的主要结果，即其解的控制分量的一个表示公式。后者适用于由外生风险产生的随机负债的证券化，这些负债通过在给定金融市场上的投资以指数偏好进行最优对冲。在纯随机形式下，FBSDE的后向分量的控制过程引导系统进入随机负债，并描述了其在资本市场上的最优衍生工具套期保值，其动力学由前向分量给出。
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英文标题：
《Differentiability of quadratic BSDEs generated by continuous martingales》
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作者：
Peter Imkeller, Anthony R\'eveillac, Anja Richter
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最新提交年份：
2012
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分类信息：

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：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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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：
  In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FBSDE with respect to the initial value of its forward component. This enables us to obtain the main result of this article, namely a representation formula for the control component of its solution. The latter is relevant in the context of securitization of random liabilities arising from exogenous risk, which are optimally hedged by investment in a given financial market with respect to exponential preferences. In a purely stochastic formulation, the control process of the backward component of the FBSDE steers the system into the random liability and describes its optimal derivative hedge by investment in the capital market, the dynamics of which is given by the forward component.
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PDF链接：
https://arxiv.org/pdf/0907.0941