鞅的实现累积量
Realized cumulants for martingales
摘要：
推广已实现方差，已实现偏度（Neuberger，2012）和已实现峰度（Bae和Lee，2020），我们构造具有所谓聚集性质的已实现累积量。它们是基于鞅及其低阶条件累积量过程的子周期增量的鞅边际累积量的无偏统计量。我们的关键发现是聚集性质与完整贝尔多项式之间的关系。对于一个应用，我们给出了Lacoin等人（2019）和Friz等人（2020）最近获得的累积量递推公式的另一种证明和扩展。
英文摘要：
Generalizing the realized variance, the realized skewness (Neuberger, 2012) and the realized kurtosis (Bae and Lee, 2020), we construct realized cumulants with the so-called aggregation property. They are unbiased statistics of the cumulants of a martingale marginal based on sub-period increments of the martingale and its lower-order conditional cumulant processes. Our key finding is a relation between the aggregation property and the complete Bell polynomials. For an application we give an alternative proof and an extension of a cumulant recursion formula recently obtained by Lacoin et al. (2019) and Friz et al. (2020).
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