分位数时钟
Quantile clocks
摘要：
分位数时钟被定义为从属子$L$与正随机变量的分位数函数的卷积。我们表明，分位数时钟可以被选择为严格增加和连续的，并讨论其实际建模的优势，在资产价格模型的业务活动时间。我们证明了分位数时钟在每个固定时刻的边缘分布与单个从属子的边缘分布是等价的。此外，我们发现，有许多分位数时钟，其中可以指定$L$，使其边缘分布有一个所需的法律类的广义$s$ -自分解分布，特别是类的自分解分布。这些结果的发展涉及元素的分布理论的特定类别的无限可分随机变量，也分解的伽玛从属，这是独立的利益。作为应用，我们构建了许多价格模型，具有连续的轨迹，表现出波动聚类，并具有边缘分布，相当于那些相当一般的指数Lévy价格模型。特别是，我们提供了明确的细节，连续过程的边际等同于流行的VG，CGMY和NIG价格模型。我们还展示了如何完美地采样的边缘分布更一般类的卷积从属时，$L$是在一个子类的广义伽玛卷积，这是相关的欧式期权定价。
英文摘要：
Quantile clocks are defined as convolutions of subordinators $L$, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling advantages as business activity times in models for asset prices. We show that the marginal distributions of a quantile clock, at each fixed time, equate with the marginal distribution of a single subordinator. Moreover, we show that there are many quantile clocks where one can specify $L$, such that their marginal distributions have a desired law in the class of generalized $s$-self decomposable distributions, and in particular the class of self-decomposable distributions. The development of these results involves elements of distribution theory for specific classes of infinitely divisible random variables and also decompositions of a gamma subordinator, that is of independent interest. As applications, we construct many price models that have continuous trajectories, exhibit volatility clustering and have marginal distributions that are equivalent to those of quite general exponential Lévy price models. In particular, we provide explicit details for continuous processes whose marginals equate with the popular VG, CGMY and NIG price models. We also show how to perfectly sample the marginal distributions of more general classes of convoluted subordinators when $L$ is in a sub-class of generalized gamma convolutions, which is relevant for pricing of European style options.
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