On the Tail Probabilities of Aggregated Lognormal Random Fields with Small Noise

• 成果类型: Article
• 署名作者: Li, Xiaoou; Liu, Jingchen; Xu, Gongjun
• 署名单位: Columbia University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0724
• 发表日期: 2016
• 页码: 236-246
• 关键词: gaussian random-fields; Value-at-risk; random-variables; brownian-motion; INTEGRALS; sums

摘要

We develop asymptotic approximations for the tail probabilities of integrals of lognormal random fields. We consider the asymptotic regime that the variance of the random field converges to zero. Under this setting, the integral converges to its limiting value. This analysis is of interest in considering short-term portfolio risk analysis (such as daily performance), for which the variances of log-returns could be as small as a few percent.