PATH DECOMPOSITION OF RUINOUS BEHAVIOR FOR A GENERAL LEVY INSURANCE RISK PROCESS

• 成果类型: Article
• 署名作者: Griffin, Philip S.; Maller, Ross A.
• 署名单位: Syracuse University; Australian National University; Australian National University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP797
• 发表日期: 2012
• 页码: 1411-1449
• 关键词: convolution equivalence; overshoots; undershoots; tails

摘要

We analyze the general Levy insurance risk process for Levy measures in the convolution equivalence class S-(alpha), alpha > 0, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level u -> infinity, and a host of new results for functionals of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as u > infinity, conditional on ruin occurring under our assumptions. Existing asymptotic results under the S-(alpha) assumption are synthesized and extended, and proofs are much simplified, by comparison with previous methods specific to the convolution equivalence analyses. Additionally, limiting expressions for penalty functions of the type introduced into actuarial mathematics by Gerber and Shiu are derived as straightforward applications of our main results.