EXIT PROBLEM OF A TWO-DIMENSIONAL RISK PROCESS FROM THE QUADRANT: EXACT AND ASYMPTOTIC RESULTS

• 成果类型: Article
• 署名作者: Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R.
• 署名单位: Universite de Pau et des Pays de l'Adour; University of Wroclaw; University of London; King's College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP529
• 发表日期: 2008
• 页码: 2421-2449
• 关键词: dependent risks; finite-time; ruin; probabilities; MODEL

摘要

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional fisk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate ruin probability. In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cramer light-tail assumption on the claim size distribution.