英文标题：
《Weak reflection principle for L\\\'evy processes》
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作者：
Erhan Bayraktar, Sergey Nadtochiy
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最新提交年份：
2015
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英文摘要：
  In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is obtained by weakening the assumptions of symmetry required for the classical reflection principle to work. We call this method a weak reflection principle and show that it provides solutions to many problems for which the classical reflection principle is typically used. In addition, unlike the classical reflection principle, the new method works for a much larger class of stochastic processes which, in particular, do not possess any strong symmetries. Here, we review the existing results which establish the weak reflection principle for a large class of time-homogeneous diffusions on a real line and then proceed to extend this method to the L\\\'{e}vy processes with one-sided jumps (subject to some admissibility conditions). Finally, we demonstrate the applications of the weak reflection principle in financial mathematics, computational methods and inverse problems.
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中文摘要：
在本文中，我们发展了一种新的数学技术，它允许我们通过过程本身的边缘分布来表达马尔可夫过程及其运行最大值（或最小值）的联合分布。这项技术是布朗运动经典反射原理的扩展，它是通过削弱经典反射原理工作所需的对称性假设而获得的。我们称这种方法为弱反射原理，并表明它为许多经典反射原理通常用于的问题提供了解决方案。此外，与经典反射原理不同，新方法适用于更大类别的随机过程，尤其是不具有任何强对称性的随机过程。在这里，我们回顾了现有的结果，这些结果建立了实线上一大类时间均匀扩散的弱反射原理，然后将此方法推广到具有单侧跳跃的L \\{e}vy过程（受某些容许条件的约束）。最后，我们展示了弱反射原理在金融数学、计算方法和反问题中的应用。
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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：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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