EXIT PROBLEM OF A TWO-DIMENSIONAL RISK PROCESS FROM THE QUADRANT: EXACT AND ASYMPTOTIC RESULTS
EXIT PROBLEM OF A TWO-DIMENSIONAL RISK PROCESS FROM THE QUADRANT: EXACT AND ASYMPTOTIC RESULTS
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DOI：
10.1214/08-aap529
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发表时间：
2008-12-01
影响因子：
1.8
通讯作者：
Pistorius, Martijn R.
中科院分区：
文献类型：
--
作者：
Avram, Florin;Palmowski, Zbigniew;Pistorius, Martijn R.
考虑两家保险公司（或同一家公司的两个分支机构），它们按特定比例分配索赔和保费。我们根据续保流程对索赔的发生进行建模。考虑的一个破产问题是相应的二维 fisk 过程首先离开正象限；另一个是进入负象限。当索赔根据泊松过程到达时，我们获得最终破产概率的封闭形式表达式。在一般情况下，我们分析了在索赔规模分布的 Cramer 轻尾假设下，当两家公司的初始准备金趋于无穷大时破产概率的渐进性。
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.