带折现率多险种离散时间风险模型的破产问题  

RUIN PROBLEMS FOR THE DISCRETE TIME INSURANCE RISK MODEL WITH DISCOUNT RATE AND MULTIPLE TYPES OF INSURANCE

作　　者：于莉[1] 詹晓琳[2] 王青芳[1] YU Li;ZHAN Xiao-lin;WANG Jing-fang(School of Management,Hefei University of Technology,Hefei 230009,China;School of Science,Shanghai Second Polytechnic University,Shanghai 201209,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230009 [2]上海第二工业大学理学院,上海201209

出　　处：《数学杂志》2020年第6期737-745,共9页Journal of Mathematics

基　　金：校社科类基金资助(JS2018HGXJ0046);2019课程思政项目-多元统计分析基金资助(119-033035);校博士专项科研基金资助(JZ2018HGBZ0108).

摘　　要：本文研究了理赔量具有一阶自回归结构以及在此条件下引入折现率和多险种的修正的离散时间金融风险模型,利用两种不同的方法,获得了破产前最大盈余、破产前盈余、破产后赤字及它们的联合分布所满足的递归式方程和破产概率所满足的积分方程,最后通过数据模拟说明了该模型的实际意义,推广了经典离散时间金融风险模型的结构和破产问题.This paper studies the revised financial risk model in discrete time when the claims havefirst-order autoregressive structure,under the conditions of this,the discount rate and multiple coverage are introduced.Using two different methods,the recursion equations of the maximum surplus before bankruptcy,bankruptcy before the surplus,deficit after bankruptcy and their joint distribution of them,and the integration equation for the ruin probability are obtained.Finally,through data simulation the practical significance of the model is illustrated,the structure and bankruptcy of the classical financial risk model in discrete time is generalized.

关 键 词：折现率 多险种 一阶自回归结构 破产后赤字 破产前盈余 破产概率 

分 类 号：O221.5[理学—运筹学与控制论]