允许赤字的MAP风险过程首达时

保险公司作为负债经营的特殊企业,其偿付能力受到监管部门的约束,本文以公司负债经营为前提研究其各种首次时.考虑MAP风险过程,即存在一随机背景Markov过程,索赔到达与索赔大小同时受这一背景过程影响,索赔到达为Markov到达点过程(MAP),索赔大小对于不同的背景状态具有不同的分布.本文给出首达时满足的积分-微分方程,通过求解带边界条件的积分-微分方程,给出了盈余过程从初始盈余水平到达某一给定盈余水平的首达时的Laplace变换的矩阵表示式,并由此推得了盈余过程到达指定水平的若干首达事件概率.

The First Passage Times in the MAP Risk Process Allow Deficit

As a special enterprise allow deficit,an insurance company＆#39;s solvency is constrained by the supervision de-partment.In this paper,we studied the various First Passage Times （FPTs）of the insurance company allow deficit.We de-scribed a MAP risk model in stochastic environment,in which,the claims arrive according to a Markovian Arrival Process （MAP）,and the distributions of the claim sizes are modulated by the background Markov process.A system of integro-dif-ferential equations with boundary conditions was derived and solved.We obtained the matrix expressions for the Laplace trans-forms of some first times that the surplus process reaches a given threshold from the initial level,and the expressions of the probabilities that the surplus process reaches a given threshold from the initial level were also derived.