英文标题：
《BSDEs with weak reflections and partial hedging of American options》
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作者：
Roxana Dumitrescu, Romuald Elie, Wissal Sabbagh, Chao Zhou
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最新提交年份：
2017
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英文摘要：
We introduce a new class of \\textit{Backward Stochastic Differential Equations with weak reflections} whose solution $(Y,Z)$ satisfies the weak constraint $\\textbf{E}[\\Psi(\\theta,Y_\\theta)] \\geq m,$ for all stopping time $\\theta$ taking values between $0$ and a terminal time $T$, where $\\Psi$ is a random non-decreasing map and $m$ a given threshold. We study the wellposedness of such equations and show that the family of minimal time $t$-values $Y_t$ can be aggregated by a right-continuous process. We give a nonlinear Mertens type decomposition for lower reflected $g$-submartingales, which to the best of our knowledge, represents a new result in the literature. Using this decomposition, we obtain a representation of the minimal time $t$-values process. We also show that the minimal supersolution of a such equation can be written as a \\textit{stochastic control/optimal stopping game}, which is shown to admit, under appropriate assumptions, a value and saddle points. From a financial point of view, this problem is related to the approximative hedging for American options.
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中文摘要：
我们引入了一类新的倒向随机微分方程，其解$（Y，Z）$满足弱约束$\\textbf{E}[\\Psi（\\theta，Y\\utheta）]\\geq m$，对于所有停止时间$\\theta$，取值范围为0$和终端时间$\\T$，其中$\\Psi$是一个随机非递减映射，m$是一个给定的阈值。我们研究了这类方程的适定性，并证明了最小时间$t$-值$Y\\U t$的族可以通过右连续过程聚合。我们给出了低反射$g$-子鞅的非线性Mertens型分解，据我们所知，这代表了文献中的一个新结果。利用这种分解，我们得到了最小时间$t$-值过程的表示。我们还证明了这样一个方程的最小上解可以写成一个{随机控制/最优停止对策}，在适当的假设下，它允许一个值和鞍点。从金融角度来看，这个问题与美式期权的近似对冲有关。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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