A truncated Lévy subordinator is a Lévy subordinator in R + with Lévy measure restricted from above by a certain level b . In this article, we study the path and distribution properties of this type of process in detail and set up an exact simulation framework based on a marked renewal process. In particular, we focus on a typical specification of truncated Lévy subordinator, namely the truncated stable process. We establish an exact simulation algorithm for the truncated stable process, which is very accurate and efficient. Compared to the existing algorithm suggested in Chi, our algorithm outperforms over all parameter settings. Using the distributional decomposition technique, we also develop an exact simulation algorithm for the truncated tempered stable process and other related processes. We illustrate an application of our algorithm as a valuation tool for stochastic hyperbolic discounting, and numerical analysis is provided to demonstrate the accuracy and effectiveness of our methods. We also show that variations of the result can also be used to sample two-sided truncated Lévy processes, two-sided Lévy processes via subordinating Brownian motions, and truncated Lévy-driven Ornstein-Uhlenbeck processes.

中文翻译：

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截断 Lévy 下属的精确模拟

截断的 Lévy 下属子是 R 中的 Lévy 下属子+Lévy 措施从上方受到一定程度的限制b. 在本文中，我们详细研究了此类过程的路径和分布特性，并建立了基于标记更新过程的精确模拟框架。特别是，我们关注截断 Lévy 从属子的典型规范，即截断稳定过程。我们为截断的稳定过程建立了一个精确的模拟算法，该算法非常准确和高效。与 Chi 中建议的现有算法相比，我们的算法优于所有参数设置。利用分布分解技术，我们还开发了截断回火稳定过程和其他相关过程的精确模拟算法。我们说明了我们的算法作为随机双曲线贴现估值工具的应用，并提供数值分析以证明我们方法的准确性和有效性。我们还表明，结果的变化也可用于对双边截断 Lévy 过程、通过从属布朗运动的双边 Lévy 过程和截断 Lévy 驱动的 Ornstein-Uhlenbeck 过程进行采样。