摘要翻译：
本文结合了各种分析方法，绘制了一个全面的画面，惩罚逼近的价值，套期保值比率，最优执行策略的美式期权。虽然对于足够光滑的障碍，惩罚解的收敛性在文献中得到了充分的证明，但尖锐的收敛速度，特别是梯度不连续（即期权收益中无处不在的“扭结”）对这一速度的影响，迄今尚未得到充分分析。这种影响变得很重要，尤其是在使用惩罚作为数字技术时。我们使用匹配渐近展开来表征行使区和持有区之间的边界层，并计算单资产在扩散或跳扩散模型下的代表性收益的一阶修正。此外，我们还演示了如何将[Jakobsen，2006]中的粘度理论框架应用于该设置，推导出该值的上下界。在[Bensoussan&Lions，1982]的小范围推广中，我们也得到了跳扩散模型下凸收益期权敏感性的弱收敛速度。最后，我们概述了结果的应用，包括通过外推提高精度。
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英文标题：
《The Effect of Non-Smooth Payoffs on the Penalty Approximation of
  American Options》
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作者：
Sam Howison, Christoph Reisinger, Jan Hendrik Witte
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最新提交年份：
2013
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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：Functional Analysis        功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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英文摘要：
  This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of convergence and particularly the effect of gradient discontinuities (i.e., the omni-present `kinks' in option payoffs) on this rate have not been fully analysed so far. This effect becomes important not least when using penalisation as a numerical technique. We use matched asymptotic expansions to characterise the boundary layers between exercise and hold regions, and to compute first order corrections for representative payoffs on a single asset following a diffusion or jump-diffusion model. Furthermore, we demonstrate how the viscosity theory framework in [Jakobsen, 2006] can be applied to this setting to derive upper and lower bounds on the value. In a small extension to [Bensoussan & Lions, 1982], we derive weak convergence rates also for option sensitivities for convex payoffs under jump-diffusion models. Finally, we outline applications of the results, including accuracy improvements by extrapolation.
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PDF链接：
https://arxiv.org/pdf/1008.0836