具有随机时滞的二元正态逆高斯过程：有效模拟及其在能源市场中的应用
A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets
摘要：
利用Gardini等人[11]中引入的自分解从属子的概念，我们建立了一个新的二元正态逆高斯过程，它可以捕获随机时滞。此外，我们还开发了一种新的路径模拟方案，该方案依赖于自分解逆高斯定律和具有逆高斯平稳分布的Lévy驱动的Ornstein-Uhlenbeck过程之间的数学联系。我们证明了我们的方法对Zhang和Zhang [23]中详细描述的现有模拟方案进行了改进，因为它不依赖于接受-拒绝方法。最后，这些结果被应用到能源市场的建模和价差期权的定价使用建议的蒙特卡罗计划和傅立叶技术
英文摘要：
Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and Lévy-driven Ornstein-Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang [23] because it does not rely on an acceptance-rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques
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