具有分红、流动储备金和利率的风险模型的绝对破产  

A Risk Model with Credit and Debit Interests,Liquid Reserves and Dividends Under Absolute Ruin

作　　者：张燕[1,2] 赵培标[2] 

机构地区：[1]解放军理工大学理学院,南京210094 [2]南京理工大学理学院,南京211101

出　　处：《经济数学》2016年第2期15-22,共8页Journal of Quantitative Economics

摘　　要：建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型.利用全概率公式和泰勒展式,推导出了该模型的Gerber-Shiu函数和绝对破产时刻的累积分红现值期望满足的积分-微分方程及边界条件,借助Volterra方程,给出了Gerber-Shiu函数的解析表达式.This paper studied the compound Poisson risk model with liquid reserves,credit interest and debit interest in the presence of a threshold dividend strategy.By the total law of probability and Taylor’s expansion,we first obtained the integro-differential equations with boundary conditions satisfying the Gerber-Shiu function and presented the closed form expressions for the Gerber-Shiu function.Secondly,we derived the integro-differential equations with boundary conditions satisfying the expected discounted present value of all dividends until absolute ruin by employing Volterra equations.

关 键 词：保险数学 GERBER-SHIU函数 积分—微分方程 分红 流动储备金 

分 类 号：O211.6[理学—概率论与数理统计]