论文标题
正常的伽马 - 帕雷托过程：一种具有柔性尾巴和跳跃特性的新型纯跳跃莱维工艺
The Normal-Generalised Gamma-Pareto process: A novel pure-jump Lévy process with flexible tail and jump-activity properties
论文作者
论文摘要
纯粹的莱维过程是流行的随机过程类别，它们在金融，统计或机器学习中发现了许多应用。在本文中，我们提出了一个新型的自我分解的莱维过程家族，其中一个人可以通过两个不同的参数分别控制尾巴行为和过程的跳跃活动。至关重要的是，我们表明可以在任何时间尺度上精确地对该过程进行精确的增量。这允许实施无似然的马尔可夫链蒙特卡洛算法（渐近）确切的后验推断。我们在基于Lévy的随机波动率模型中使用这种新型过程来预测股票市场数据的回报，并表明与经典替代方案相比，所提出的一类模型可以提高卓越的预测性能。
Pure-jump Lévy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable Lévy processes where one can control separately the tail behavior and the jump activity of the process, via two different parameters. Crucially, we show that one can sample exactly increments of this process, at any time scale; this allows the implementation of likelihood-free Markov chain Monte Carlo algorithms for (asymptotically) exact posterior inference. We use this novel process in Lévy-based stochastic volatility models to predict the returns of stock market data, and show that the proposed class of models leads to superior predictive performances compared to classical alternatives.
