On exact sampling of the first passage event of a Levy process with infinite Levy measure and bounded variation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Chi, Zhiyi¹ 

[1] Univ Connecticut, Dept Stat, Storrs, CT 06269 USA

关键词: First passage;    Levy process;    Bounded variation;    Subordinator;    Creeping;    Dirichlet distribution;   

DOI  :  10.1016/j.spa.2015.11.001

来源: Elsevier

【 摘 要 】

Exact sampling of the first passage event (FPE) of a Levy process with infinite Levy measure is challenging due to lack of analytic formulas. We present an approach to the sampling for processes with bounded variation. The idea is to embed a process for which we wish to sample the FPE into another process whose FPE can be sampled based on analytic formulas, and once the latter FPE is sampled, extract from it the part belonging to the former process. We obtain general procedures to sample the FPE across a regular nonincreasing boundary or out of an interval. Concrete algorithms are given for two important classes of Levy processes. The approach is based on distributional results that appear to be new. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free