论文标题
已实现的累积者
Realized cumulants for martingales
论文作者
论文摘要
概括了已实现的偏度（Neuberger，2012）和已实现的峰度（Bae和Lee，2020年），我们用所谓的聚集特性构建了实现的累积物。它们是基于Martingale的子周期增量及其低阶条件累积过程的Mardingale边缘累积物的公正统计数据。我们的关键发现是聚合属性与完整的铃铛多项式之间的关系。对于应用，我们给出了Lacoin等人最近获得的累积递归公式的替代证明和扩展。 （2019）和Friz等。 （2020）。
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).
