允许赤字的MAP风险过程首达时

张超权; 刘晓辉

允许赤字的MAP风险过程首达时

引用本文：张超权，刘晓辉.允许赤字的MAP风险过程首达时[J].经济数学,2014,(4):36-40

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作者	单位
张超权，刘晓辉	（桂林航天工业学院理学部，广西桂林 541004）

中文摘要: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.

中文关键词:风险过程首达时 Laplace变换积分-微分方程

The First Passage Times in the MAP Risk Process Allow Deficit

Abstract:As a special enterprise allow deficit, an insurance company's solvency is constrained by the supervision department. In this paper, we studied the various First Passage Times (FPTs) of the insurance company allow deficit. We described 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-differential equations with boundary conditions was derived and solved. We obtained the matrix expressions for the Laplace transforms 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.

keywords:risk process first passage times Laplace transform integro-differential equation

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