Exact simulation of generalised Vervaat perpetuities
Exact simulation of generalised Vervaat perpetuities
复制标题
广义 Vervaat 永续年金的精确模拟
DOI：
10.1017/jpr.2019.6
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发表时间：
2019
影响因子：
1
通讯作者：
Jia Wei Lim
中科院分区：
文献类型：
--
作者：
A. Dassios;Yan Qu;Jia Wei Lim
摘要考虑X = Y1W1 +Y2W1W2 +···的广义Vervaat永续性，其中$W_i \sim {\cal U}^{1/t}$和（Yi）i≥0是独立于（Wi）i≥0的随机变量的独立同分布序列。基于分布分解技术，提出了一种精确模拟广义Vervaat永续性的新方法。一般框架依赖于截断伽马过程的精确模拟，我们使用标记的更新表示来开发其路径。此外，当Yi = 1，且X具有广义Dickman分布时，我们提出了一种使用标记更新方法的精确模拟算法。特别是，这种新算法比Chi (2012), Cloud and Huber (2017), Devroye and Fawzi（2010）以及Fill and Huber（2010）中所述的现有算法快得多，并且适用于一般支付情况。算例和数值分析验证了该方法的准确性和有效性。
Abstract We consider a generalised Vervaat perpetuity of the form X = Y1W1 +Y2W1W2 + · · ·, where $W_i \sim {\cal U}^{1/t}$ and (Yi)i≥0 is an independent and identically distributed sequence of random variables independent from (Wi)i≥0. Based on a distributional decomposition technique, we propose a novel method for exactly simulating the generalised Vervaat perpetuity. The general framework relies on the exact simulation of the truncated gamma process, which we develop using a marked renewal representation for its paths. Furthermore, a special case arises when Yi = 1, and X has the generalised Dickman distribution, for which we present an exact simulation algorithm using the marked renewal approach. In particular, this new algorithm is much faster than existing algorithms illustrated in Chi (2012), Cloud and Huber (2017), Devroye and Fawzi (2010), and Fill and Huber (2010), as well as being applicable to the general payments case. Examples and numerical analysis are provided to demonstrate the accuracy and effectiveness of our method.