Ruin probabilities and overshoots for general Levy insurance risk processes
Ruin probabilities and overshoots for general Levy insurance risk processes
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DOI：
10.1214/105051604000000927
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发表时间：
2004-11-01
影响因子：
1.8
通讯作者：
Maller, RA
中科院分区：
文献类型：
--
作者：
Klüppelberg, C;Kyprianou, AE;Maller, RA
我们在一般Levy过程设置中制定了保险风险过程，并给出了当过程漂移到-无穷大时破产概率和过程超调高于高水平的渐近分布的一般定理。 Levy 度量或梯子高度度量的正尾部是次指数的，或者更一般地说，是卷积等价的。 Asmussen 和 Kluppelberg 的结果 [随机过程。应用。 64 (1996) 103-125] 以及 Bertoin 和 Doney [Adv. 64 (1996) 103-125]在应用程序中。很可能。 28 (1996) 207-226] 对于随机游走和复合泊松模型中的破产概率和超调，显示在一般设置中具有类似物。我们得出的恒等式为进一步研究 Levy 过程的一般更新型属性开辟了道路。
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.