摘要翻译：
本文在百慕大期权对偶估值的背景下，引入并研究了最优对偶鞅和肯定最优对偶鞅的概念，并概述了在这一背景下新算法的发展。我们给出了一个刻画定理，一个给出鞅肯定最优条件的定理，以及一个关于在某种意义上接近肯定最优的鞅的稳定性定理。在这些结果的指导下，我们发展了一个构造这类鞅的反向算法框架。反过来，这个鞅可以用来计算百慕大乘积的上界。这种方法是纯对偶的，因为它不需要一定的Snell包络的输入近似。在IT环境下，我们提出了一种特殊的基于回归的反向算法，该算法不需要嵌套蒙特卡罗模拟就可以计算对偶上界。此外，作为一个副产品，该算法还提供了乘积的连续值的近似值，这反过来又决定了停止策略。因此，我们可以同时得到下界。在第一个数值研究中，我们在Wiener环境下，在众所周知的基准示例中演示了向后对偶回归算法。事实证明，该方法至少可以与Belomestny et的方法相媲美。Al.(2009)在精确度方面，但在计算健壮性方面，甚至有几个优点。
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英文标题：
《Optimal dual martingales, their analysis and application to new
  algorithms for Bermudan products》
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作者：
John Schoenmakers, Junbo Huang, Jianing Zhang
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最新提交年份：
2012
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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：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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英文摘要：
  In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optimal, and a stability theorem concerning martingales which are near to be surely optimal in a sense. Guided by these results we develop a framework of backward algorithms for constructing such a martingale. In turn this martingale may then be utilized for computing an upper bound of the Bermudan product. The methodology is pure dual in the sense that it doesn't require certain input approximations to the Snell envelope. In an It\^o-L\'evy environment we outline a particular regression based backward algorithm which allows for computing dual upper bounds without nested Monte Carlo simulation. Moreover, as a by-product this algorithm also provides approximations to the continuation values of the product, which in turn determine a stopping policy. Hence, we may obtain lower bounds at the same time. In a first numerical study we demonstrate the backward dual regression algorithm in a Wiener environment at well known benchmark examples. It turns out that the method is at least comparable to the one in Belomestny et. al. (2009) regarding accuracy, but regarding computational robustness there are even several advantages.
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PDF链接：
https://arxiv.org/pdf/1111.6038