带借贷利率和门槛分红策略的Erlang(n)盈余过程（英文）  

Erlang(n) Surplus Process with Debit Interest and a Threshold Dividend Strategy

作　　者：赵一惠 罗葵 肖立群 明瑞星[1] 胡亦钧[4] ZHAO Yihui;LUO Kui XIAO Liqun;MING Ruixing;HU Yijun(School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;Industrial Training Centre, Shenzhen Polytechnic, Shenzhen 518055, China;School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]深圳职业技术学院工业训练中心,广东深圳518055 [3]广州大学经济与统计学院,广东广州510006 [4]武汉大学数学与统计学院,湖北武汉430072

出　　处：《应用数学》2018年第3期714-722,共9页Mathematica Applicata

基　　金：Foundation item:Supported by National Science Foundation of China(Grant 11601097);Zhejiang Provincial Natural Science Foundation of China(LY16A010001);Zhejiang Provincial Key Research Base for Humanities and Social Sciences Grant(statistics);Zhejiang Educational Committee(1020KZ0413455)

摘　　要：本文考虑带借贷利率和门槛分红策略的Erlang(n)盈余过程:当保险公司的盈余为负数时,允许保险公司以某借贷利率向银行借贷以继续经营业务;当保险公司的盈余超过某个正的门槛值时,保险公司将向其股东支付红利.我们研究了绝对破产时支付红利现值的矩母函数和m阶矩函数.特别地,在Erlang(2)盈余情形下,当索赔额的分布服从指数分布时,我们得到总分红现值的精确解析式;并且利用数值模拟的方法对参数进行了敏感性分析.In this paper, we consider the Erlang（n） surplus process with debit interest and a threshold dividend strategy. When the surplus is negative, an insurance company is allowed to borrow money to continue its business at a certain debit interest rate. When the surplus is above a given threshold level, the company pays part of the premium income as dividends to shareholders. We study the moment generating function and the m-th moment function of the discounted sum of dividend payments until absolute ruin. Explicit results of the expected accumulated discounted dividends until absolute ruin for the case of the Erlang（2） surplus process with exponential claim amount distribution are obtained.Moreover, numerical illustrations of the expected accumulated discounted dividends until absolute ruin are used to identify the influence of parameters.

关 键 词：Erlang(n)盈余过程 绝对破产概率 门槛分红策略 期望折扣惩罚函数 矩母函数 

分 类 号：O211.6[理学—概率论与数理统计]