Tail Analysis Without Parametric Models: A Worst-Case Perspective

• 成果类型: Article
• 署名作者: Lam, Henry; Mottet, Clementine
• 署名单位: Columbia University; Boston University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1643
• 发表日期: 2017
• 页码: 1696-1711
• 关键词: portfolio credit risk; distributionally robust optimization; multivariate convex regression; maximum-likelihood-estimation; concave density; fast simulation; extreme-points; inequalities; inference; systems

摘要

A common bottleneck in evaluating extremal performance measures is that, because of their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric fitting, but the validity of the parametric choice can be difficult to verify. This paper describes an alternative based on the computation of worst-case bounds under the geometric premise of tail convexity, a feature shared by all common parametric tail distributions. We characterize the optimality structure of the resulting optimization problem, and demonstrate that the worst-case convex tail behavior is in a sense either extremely light tailed or extremely heavy tailed. We develop low-dimensional nonlinear programs that distinguish between the two cases and compute the worst-case bound. We numerically illustrate how the proposed approach can give more reliable performances than conventional parametric methods.