英文标题：
《On robust pricing-hedging duality in continuous time》
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作者：
Zhaoxu Hou, Jan Obloj
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最新提交年份：
2015
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英文摘要：
  We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland (2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices is equal to supremum over calibrated martingale measures. In presence of non-trivial beliefs, the equality is between limiting values of perturbed problems. In particular, our results include the martingale optimal transport duality of Dolinsky and Soner (2013) and extend it to multiple dimensions and multiple maturities.
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中文摘要：
我们在数学金融领域追求稳健的定价和对冲方法。我们考虑一个连续时间设置，其中一些具有连续路径的基础资产和期权可用于动态交易，而另一组欧洲期权（可能具有不同的到期日）可用于静态交易。受Mykland（2003）中预测集概念的启发，我们通过允许指定一组要考虑的路径，将建模信念包括在我们的设置中，例如，只有属于给定集的路径才需要超级复制未定权益。因此，我们的框架在独立于模型和特定于模型的设置之间进行插值，并允许量化做出假设或获取信息的影响。我们得到了一个一般的定价套期保值对偶结果：超边际价格上的下确界等于校准鞅测度上的上确界。在存在非平凡信念的情况下，等式是扰动问题的极限值之间的等式。特别是，我们的结果包括了Dolinsky和Soner（2013）的鞅最优运输对偶，并将其推广到多个维度和多个到期日。
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分类信息：

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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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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