CONVOLUTION EQUIVALENT LEVY PROCESSES AND FIRST PASSAGE TIMES

• 成果类型: Article
• 署名作者: Griffin, Philip S.
• 署名单位: Syracuse University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP879
• 发表日期: 2013
• 页码: 1506-1543
• 关键词: ruin probabilities; distributions; functionals; undershoots; overshoots; BEHAVIOR

摘要

We investigate the behavior of Levy processes with convolution equivalent Levy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial reserve. We obtain a precise asymptotic estimate on the probability of first passage occurring by time T. This result is then used to study the process conditioned on first passage by time T. The existence of a limiting process as u -> infinity is demonstrated, which leads to precise estimates for the probability of other events relating to first passage, such as the overshoot. A discussion of these results, as they relate to insurance risk, is also given.