论文标题
用依赖相类型索赔破坏风险过程的问题
Ruin problems for risk processes with dependent phase-type claims
论文作者
论文摘要
我们考虑持续的时间风险过程，其中索赔大小取决于且非相同分布的相位类型分布。我们提出的分布类别很容易表征，并允许以简单和直观的方式合并主张之间的依赖性。它还旨在通过使用Markov改编的流体嵌入技术来促进风险过程的研究。使用此技术，我们获得了简单的递归程序，以确定废墟时间的关节分布，废墟的赤字以及废墟前的索赔数量。我们还获得了一些最终破坏概率的界限。最后，我们提供了一些多元相型分布的示例，并将其用于数值插图。
We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the dependence between claims in a simple and intuitive way. It is also designed to facilitate the study of the risk processes by using a Markov-modulated fluid embedding technique. Using this technique, we obtain simple recursive procedures to determine the joint distribution of the time of ruin, the deficit at ruin and the number of claims before the ruin. We also obtain some bounds for the ultimate ruin probability. Finally, we provide a few examples of multivariate phase-type distributions and use them for numerical illustration.
