摆动期权定价的一阶BSPDE：经典解
A First-Order BSPDE for Swing Option Pricing: Classical Solutions
摘要：
在Bender and 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倒向SPDE和路径微分包含唯一刻画。在本文中，我们还假设摆动期权的现金流过程是左连续的期望（LCE）。在这个假设下，我们证明了价值过程在空间变量中是连续可微的，空间变量代表期权持有者在到期前仍然可以行使的数量。这就产生了一个存在性和唯一性的结果，相应的向后SPDE在一个经典的意义。我们还明确表示的空间导数的价值过程中的一个非标准的最优停时问题的一个子集的可预测的停时。这种表示可以用来导出一个关于鞅的对偶极小化问题。
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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