Ruin probabilities and overshoots for general Levy insurance risk processes

• 成果类型: Article
• 署名作者: Klüppelberg, C; Kyprianou, AE; Maller, RA
• 署名单位: Technical University of Munich; Utrecht University; Australian National University; Australian National University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000927
• 发表日期: 2004
• 页码: 1766-1801
• 关键词: random-walk; distributions; THEOREMS

摘要

We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to -infinity a.s. and the positive tail of the Levy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Kluppelberg [Stochastic Process. Appl. 64 (1996) 103-125] and Bertoin and Doney [Adv. in Appl. Probab. 28 (1996) 207-226] for ruin probabilities and the overshoot in random walk and compound Poisson models are shown to have analogues in the general setup. The identities we derive open the way to further investigation of general renewal-type properties of Levy processes.