A WIENER-HOPF MONTE CARLO SIMULATION TECHNIQUE FOR LEVY PROCESSES

• 成果类型: Article
• 署名作者: Kuznetsov, A.; Kyprianou, A. E.; Pardo, J. C.; van Schaik, K.
• 署名单位: York University - Canada; University of Bath; CIMAT - Centro de Investigacion en Matematicas
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP746
• 发表日期: 2011
• 页码: 2171-2190
• 关键词: 1st

摘要

We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Levy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr's so-called Canadization technique as well as Doney's method of stochastic bounds for Levy processes; see Carr [Rev. Fin. Studies 11 (1998) 597-626] and Doney [Ann. Probab. 32 (2004) 1545-1552]. We rely fundamentally on the Wiener-Hopf decomposition for Levy processes as well as taking advantage of recent developments in factorization techniques of the latter theory due to Vigon [Simplifiez vos Levy en titillant la factorization de Wiener-Hopf (2002) Laboratoire de Mathematiques de L'INSA de Rouen] and Kuznetsov [Ann. Appl. Probab. 20 (2010) 1801-1830]. We illustrate our Wiener-Hopf Monte Carlo method on a number of different processes, including a new family of Levy processes called hypergeometric Levy processes. Moreover, we illustrate the robustness of working with a Wiener-Hopf decomposition with two extensions. The first extension shows that if one can successfully simulate for a given Levy processes then one can successfully simulate for any independent sum of the latter process and a compound Poisson process. The second extension illustrates how one may produce a straightforward approximation for simulating the two-sided exit problem.