带阈值分红策略干扰对偶风险模型的红利支付及相关问题  

Dividend payments and relevant problems in the dual risk model with dividend threshold and diffusion

作　　者：江五元 曹聪[2] 黄俊 JIANG Wu-yuan;CAO Cong;HUANG Jun(Department of Economics and Management,Hunan Institute of Science and Technology,Yueyang 414006,China;Department of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院经济与管理学院,湖南岳阳414006 [2]湖南理工学院数学学院,湖南岳阳414006

出　　处：《高校应用数学学报（A辑）》2022年第2期217-225,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：湖南省自然科学基金(2020JJ4329);湖南省社会科学基金(18YBA198);湖南省学位与研究生教育改革项目(2020JGYB239)。

摘　　要：考虑了阈值红利策略情形下带干扰项的复合泊松风险过程的对偶模型,建立了直到破产时期望折现红利支付及相关变量满足的积分-微分方程.假设收入量分别服从指数分布和混合指数分布时,得到了期望折现红利支付的解析表达式.最后,进行了数值模拟.The dual model of the compound Poisson risk model with dividend threshold and diffusion is considered.The integro-differential equations satisfied by the expectation of discounted dividend payments until the ruin time and relevant variables are obtained.The explicit expressions of the expectation of discounted dividend payments are derived when the gain follows an exponential distribution and mixtures of exponential distributions,respectively.Finally,numerical illustrations are presented.

关 键 词：对偶风险模型 红利策略 扩散过程 指数分布 

分 类 号：O211.6[理学—概率论与数理统计]