数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 631-640.
• 论文 • 上一篇
收稿日期:
2020-11-17
出版日期:
2022-04-26
发布日期:
2022-04-18
通讯作者:
刘海燕
E-mail:rain6397@163.com
基金资助:
Mi Chen1,2,3,Changwei Nie1,Haiyan Liu1,2,*()
Received:
2020-11-17
Online:
2022-04-26
Published:
2022-04-18
Contact:
Haiyan Liu
E-mail:rain6397@163.com
Supported by:
摘要:
该文将随机保费收入、相依索赔以及随机分红策略引入到复合二项风险模型中, 并研究该模型下的随机分红问题. 运用母函数的方法, 推导得到保险公司直至破产前的期望累积折现分红量满足的差分方程及其解. 最后, 通过几个数值例子展示了所得结果.
中图分类号:
陈密,聂昌伟,刘海燕. 一类离散相依索赔风险模型的随机分红问题[J]. 数学物理学报, 2022, 42(2): 631-640.
Mi Chen,Changwei Nie,Haiyan Liu. Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims[J]. Acta mathematica scientia,Series A, 2022, 42(2): 631-640.
表 1
$b=3$, $q_0=0.8$, $q=0.1$, $\theta=0.6$, $\beta=0.7$, $\gamma=0.6$时, $V(u, b)$的值"
| |||||||||
1.3615 | 1.6118 | 1.8653 | 2.0968 | 2.1991 | 2.2684 | 2.3146 | 2.3449 | 2.3649 | |
0.6677 | 0.8219 | 0.9908 | 1.1639 | 1.2221 | 1.2614 | 1.2873 | 1.3041 | 1.3150 | |
0.3999 | 0.5123 | 0.6439 | 0.7910 | 0.8309 | 0.8579 | 0.8579 | 0.8873 | 0.8950 |
表 2
$b=8$, $v=0.93$, $q_0=0.9$, $q=0.2$, $q_1=0.2$, $\beta=\gamma=1$时, $V(u, b)$的值"
0.7612 | 0.9249 | 1.0882 | 1.2519 | 1.4327 | 1.6373 | 1.8703 | 2.1362 | 2.4399 | |
0.7121 | 0.8950 | 1.0591 | 1.2205 | 1.3975 | 1.5972 | 1.8246 | 2.0840 | 2.3803 | |
0.6689 | 0.8687 | 1.0336 | 1.1930 | 1.3665 | 1.5620 | 1.7845 | 2.0382 | 2.3279 | |
0.6307 | 0.8454 | 1.0109 | 1.1686 | 1.3391 | 1.5309 | 1.7489 | 1.9976 | 2.2816 | |
0.5966 | 0.8246 | 0.9908 | 1.1468 | 1.3147 | 1.5031 | 1.7172 | 1.9614 | 2.2403 |
表 3
$v=0.93$, $q_0=0.9$, $q=0.2$, $q_1=0.2$, $\theta=0.5$, $\beta=0.7$, $\gamma=0.8$时, $V(u, b)$的值"
| 1.6893 | 1.4971 | 1.3001 | 1.1123 | 0.9449 | 0.8003 | 0.6765 | 0.5710 | 0.4816 | 0.4058 |
1.9841 | 1.9125 | 1.6609 | 1.4209 | 1.2072 | 1.0223 | 0.8642 | 0.7296 | 0.6153 | 0.5184 | |
2.2042 | 2.1461 | 2.0305 | 1.7371 | 1.4759 | 1.2499 | 1.0565 | 0.8919 | 0.7522 | 0.6338 | |
2.3646 | 2.3201 | 2.2204 | 2.0786 | 1.7660 | 1.4955 | 1.2641 | 1.0672 | 0.9001 | 0.7584 | |
2.4837 | 2.4489 | 2.3625 | 2.2405 | 2.0902 | 1.7701 | 1.4963 | 1.2632 | 1.0654 | 0.8976 |
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