Asymptotics for ruin probabilities in Levy-driven risk models with heavy tailed claims
Asymptotics for ruin probabilities in Levy-driven risk models with heavy tailed claims
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DOI：
10.3934/jimo.2017044
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发表时间：
2017-04
影响因子：
1.3
通讯作者：
Yang Yang-Yang;K. Yuen;Jun-feng Liu
中科院分区：
文献类型：
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作者：
Yang Yang-Yang;K. Yuen;Jun-feng Liu
考虑一个二元Levy驱动的风险模型，其中保险公司的损失过程和投资收益过程是两个独立的Levy过程。在损失过程具有一致变差的Levy测度和收益过程满足一定条件的假设下，研究了有限时间破产概率的渐近性态.在损失过程仍为Levy过程，而投资收益过程为确定性线性函数的情形下，得到了单Levy驱动风险模型的有限时间破产概率和无限时间破产概率的两个渐近公式.在这样一个特殊的模型中，我们放宽了损失过程的跳，其公共分布是长尾的和控制的变化。
Consider a bivariate Levy-driven risk model in which the loss process of an insurance company and the investment return process are two independent Levy processes. Under the assumptions that the loss process has a Levy measure of consistent variation and the return process fulfills a certain condition, we investigate the asymptotic behavior of the finite-time ruin probability. Further, we derive two asymptotic formulas for the finite-time and infinite-time ruin probabilities in a single Levy-driven risk model, in which the loss process is still a Levy process, whereas the investment return process reduces to a deterministic linear function. In such a special model, we relax the loss process with jumps whose common distribution is long tailed and of dominated variation.