论文标题
相类型的近似受到重型组件的扰动，用于与双面跳跃的风险过程的gerber-shiu函数
Phase-type approximations perturbed by a heavy-tailed component for the Gerber-Shiu function of risk processes with two-sided jumps
论文作者
论文摘要
我们在本文中考虑了风险储备流程，根据两个独立的泊松过程，索赔和收益到达。尽管增益大小是相型分布的，但我们假设索赔大小是相型的，由重尾组件扰动。也就是说，索赔尺寸分布被正式选择为具有较大概率$ 1-ε$的相类型，并用少量概率$ε$进行重尾。我们分析了编码毁灭性时间的关节分布，毁灭前的剩余时间以及毁灭时的赤字。我们以已知系数为$ε$的功率来得出其作为扩展的价值，并从上述序列的前两个术语中构建了近似值。主要思想是基于所谓的流体嵌入，它允许将所考虑的风险过程纳入频谱负面的 - 马尔可夫添加过程的框架中，并使用其在Ivanovs和Palmowski（2012）中开发的波动理论。
We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type perturbed by a heavy-tailed component; that is, the claim size distribution is formally chosen to be phase-type with large probability $1-ε$ and heavy-tailed with small probability $ε$. We analyze the seminal Gerber-Shiu function coding the joint distribution of the time to ruin, the surplus immediately before ruin, and the deficit at ruin. We derive its value as an expansion with respect to powers of $ε$ with known coefficients and we construct approximations from the first two terms of the aforementioned series. The main idea is based on the so-called fluid embedding that allows to put the considered risk process into the framework of spectrally negative Markov-additive processes and use its fluctuation theory developed in Ivanovs and Palmowski (2012).
