英文标题：
《A First-Order BSPDE for Swing Option Pricing: Classical Solutions》
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作者：
Christian Bender and Nikolai Dokuchaev
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最新提交年份：
2014
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英文摘要：
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise differential inclusion. In the present paper we additionally assume that the cashflow process of the swing option is left-continuous in expectation (LCE). Under this assumption we show that the value process is continuously differentiable in the space variable that represents the volume which the holder of the option can still exercise until maturity. This gives rise to an existence and uniqueness result for the corresponding backward SPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales.
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中文摘要：
在Bender和Dokuchaev（2013）中，我们研究了一般非马尔可夫环境下与摆动期权定价相关的控制问题。主要结果表明，该控制问题的值过程可以用一阶向后SPDE和路径微分包含唯一地刻画。在本文中，我们还假设摆动期权的现金流过程在期望值（LCE）中是连续的。在此假设下，我们证明了价值过程在空间变量中是连续可微的，该空间变量表示期权持有人在到期前仍可以行使的数量。这在经典意义上给出了相应的后向SPDE的存在唯一性结果。我们还明确表示了价值过程的空间导数，即非标准最优停止问题在可预测停止时间子集上的导数。这种表示可以用来导出一个关于鞅的对偶极小化问题。
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分类信息：

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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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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