带有利率、流动性盈余和常数边界分红策略的风险模型(英文)  

The Risk Model with Interest,Liquid Reserves and a Constant Dividend Barrier

作　　者：危佳钦[1] 仇春涓[1] 

机构地区：[1]华东师范大学金融与统计学院,上海200241

出　　处：《应用概率统计》2012年第5期535-550,共16页Chinese Journal of Applied Probability and Statistics

基　　金：supported by National Natural Science Foundation of China(10971068);Doctoral Program Foundation of the Ministry of Education of China(20110076110004);Program for New Century Excellent Talents in University(NCET-09-0356);"Fundamental Research Funds for the Central Universities"

摘　　要：在这篇文章中,我们将考虑带有利率、流动性盈余和常数边界分红策略的风险模型.当保险人的盈余水平低于一个固定的值,盈余作为流动性资产、不能获取任何利息;当盈余达到某个较高的水平,盈余会以一个常值利息力赚取利息;当盈余达到一个更高的水平,超出这个水平的盈余作为红利派发给股东.我们得到了Gerber-Shiu函数满足的积分-微分方程,并得到了它的解.当理赔量分布为指数分布时,我们得到贴现率为零的Gerber-Shiu函数的精确解.我们还得到到破产时刻为止的累计贴现分红期望满足的积分-微分方程,这个量可以用来分析最优常数边界分红策略.在理赔量服从指数分布时,我们也得到了它的精确解.In this paper, we consider the compound Poisson surplus model with interest, liquid reserves and a constant dividend barrier. When the surplus of an insurer is below a fixed level, the surplus is kept as liquid reserves, which does not earn interest. When the surplus attains the level, the surplus will receive interest at a constant rate. When the surplus hits another fixed higher lever, the excess of the surplus over this higher level will be distributed to the shareholders as dividends. We derive a system of integro-differential equations for the Gerber-Shiu discounted penalty function and obtain the solutions to these integro-differential equations. In the case where the claim sizes axe exponential distributed, we get the exact solutions of zero discounted Gerber-Shiu function. We also get the integro-differential equation for the expectation of the discounted dividends until ruin which is the key to discuss the optimal dividend barrier. And we give the exact solution in the special case with exponential claim sizes.

关 键 词：常数边界分红策略 复合泊松模型 流动性盈余 积分-微分方程. 

分 类 号：O211.67[理学—概率论与数理统计]