经典风险模型中有限时间区间分红问题  

Dividend Problems for Finite Time Interval in the Classical Risk Model

作　　者：王翠莲 刘晓 WANG Cuilian;LIU Xiao(School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241002, China)

机构地区：[1]安徽师范大学数学与统计学院,芜湖241002

出　　处：《应用概率统计》2019年第2期193-199,共7页Chinese Journal of Applied Probability and Statistics

基　　金：教育部人文社科项目(批准号:17YJC910009)资助;安徽省自然科学基金项目(批准号:1908085MA21);安徽高校自然科学研究项目(批准号:KJ2018A0305);安徽师范大学博士科研启动金(批准号:2016XJJ119);安徽师范大学科研培育基金(批准号:2016XJJ004;2015xmpy14;2016XJJ055)资助

摘　　要：本文研究经典风险模型中有限时间区间分红问题.假设在时间区间[0,t]内,分红按照barrier策略支付,即给定一个非负barrier值b,仅当盈余超过b时,将超过的部分支付分红.利用微分法,得到了[0,t]内期望折现分红(V(x;t))满足的方程,并在指数理赔假设下给出了V(x;t)关于t的Laplace变换的显式表达式.最后,使用Stehfest方法给出一个数值例子.In this paper, we study the dividend problems for finite time interval in the classical risk model. Assume that the dividends are paid according to a barrier strategy in the time interval [0,t],i.e., given a nonnegative barrier value b, the dividends only can be paid when the surplus exceeds b and the excess is paid as dividend. Applying the "differential argument",the equation for the total expected discounted dividends in the time interval [0,t](V(x;t)) is derived, and the explicit expression for the Laplace transform of V(x;t) with respect to t is obtained under the assumption that the claim sizes are exponentially distributed. Finally, a numerical example is given by Stehfest method.

关 键 词：分红 有限时间区间 LAPLACE变换 Stehfest方法 

分 类 号：O212.62[理学—概率论与数理统计]