摘要
本文研究了保险公司在允许借贷和分红情况下的最优分红策略.利用HJB方法,先得到满足使分红总现值最大化的分红策略,然后针对门槛分红策略得到分红总现值满足的微积分方程,再在指数索赔分布下获得了分红总现值的精确表达式,最后证明门槛分红策略是最优的分红策略,并得到了最优的分红起始值.
In this paper, we study the optimal dividend strategy for an insurance company with debit interest and dividend payments. By HJB methods, a rule for choosing the strategy that maximizes the expected accumulated discounted dividends until absolute ruin is given. Under the so called threshold strategy, we derive integro-differential equations for the expected accumulated discounted dividends until absolute ruin. Then, explicit expressions for the expected accumulated discounted dividends until absolute ruin with exponential claim amounts are obtained. Finally,based on the explicit expressions, we prove that the optimal strategy is a threshold strategy and the optimal level of threshold is also obtained.
作者
罗葵
刘娟
赵一惠
肖立群
LUO Kui;LIU Juan;ZHAO Yi-hui;XIAO Li-qun(Industrial Training Centre,Shenzhen Polytechnic,Shenzhen 518055,China;School of Mathematics and Statistics,Guangdong University of Finance and Economic,Guangzhou 510320,China;School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)
出处
《数学杂志》
2019年第6期801-810,共10页
Journal of Mathematics
基金
Supported by National Science Foundation of China(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)
关键词
借贷利率
门槛分红策略
最优策略
期望折扣惩罚函数
debit interest
threshold dividend strategy
optimal strategy
the expected discounted penalty function
