您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (09): 78-83.doi: 10.6040/j.issn.1671-9352.0.2014.373

• 论文 • 上一篇    下一篇

带分红的稀疏风险模型的期望折现罚金函数

陈洁1, 吕玉华2   

  1. 1. 济宁学院数学系, 山东 济宁 273155;
    2. 曲阜师范大学数学科学学院, 山东 曲阜 273165
  • 收稿日期:2014-08-14 修回日期:2015-07-22 出版日期:2015-09-20 发布日期:2015-09-26
  • 作者简介:陈洁(1985-), 女, 硕士, 讲师, 研究方向为随机过程.E-mail:jiechen6688@163.com
  • 基金资助:
    国家自然科学基金资助项目(11171179);山东省自然科学基金资助项目(ZR2009AL015)

Discounted penalty function for a thinning risk model with dividend

CHEN Jie1, LÜ Yu-hua2   

  1. 1. Department of Mathematics, Jining University, Jining 273155, Shandong, China;
    2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
  • Received:2014-08-14 Revised:2015-07-22 Online:2015-09-20 Published:2015-09-26

摘要: 考虑一类带分红的稀疏风险模型,得到了期望折现罚金函数的积分微分方程。当保费额与索赔额同为指数分布时,研究了积分微分方程的拉普拉斯变换的解以及破产概率、赤字分布、破产时刻的瞬间盈余分布的积分微分方程的显解。

关键词: 障碍分红, 稀疏, 拉普拉斯变换, 期望折现罚金函数, 积分微分方程

Abstract: The thinning risk model with barrier dividend was considered. The integro-differential equation for the expected discounted penalty function was obtained. If the premium and the claim sizes are exponentially distributed, some expressions for the Laplace transform of the integro-differential equation were founded. When the premium and the claim sizes are exponentially distributed, the closed-form solutions of the time of ruin, the deficit at ruin and the surplus before ruin were obtained.

Key words: barrier dividend, Laplace transform, integro-differential equation, thinning process, expected discounted penalty function

中图分类号: 

  • O211.6
[1] AMBAGASPITIYA R S. On the distribution of two classes of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1999, 24(3):301-308.
[2] AMBAGASPITIYA R S. On the distribution of a sum of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1998, 23(1):15-19.
[3] YUEN K C, GUO Junyi. Ruin probabilities for time-correlated claims in the compound binomial model[J]. Insurance: Mathematics and Economics, 2001, 29(1):47-57.
[4] XIAO Yuntao, GUO Junyi. The compound binomial risk model with time-correlated claims[J]. Insurance: Mathematics and Economics, 2007, 41(1):124-133.
[5] AMBAGASPITIYA R S. On the distribution of a sum of correlated aggregate claims[J]. Insurance: Mathematics and Economics, 1998, 23(1):15-19.
[6] ALBRECHER H J, BOXMA O J. A ruin model with dependence between claim sizes and claim intervals[J]. Insurance: Mathematics and Economics, 2004, 35:245-254.
[7] PAN Jie, WANG Guojing. Expected discounted penalty function for a thinning risk model[J]. Chinese Journal of Applied Probability and Statistics, 2009, 25(5):544-552.
[8] 黄玉娟,于广华. 稀疏过程下保费与理赔相关的风险模型的破产概率[J].山东大学学报:理学版,2011,46(7):56-59. HUANG Yujuan, YU Guanghua. Ruin probability for a risk model with dependence between premium and claim under the thinning process[J]. Journal of Shandong University: Natural Science, 2011, 46(7):56-59.
[9] BOIKOV A V. The Cramer-Lundberg model with stochastic premium process[J].Theory of Probability and its Application, 2003, 47(3):489-493.
[10] 陈珊萍,王过京,王振羽.稀疏过程在保险公司破产问题中的应用[J].数理统计与管理, 2001, 20(5):26-30. CHEN Shanping, WANG Guojing, WANG Zhenxu. The application of thinning process in risk problem[J].Chinese Journal of Application of Statistics and Management, 2001, 20(5):26-30.
[1] 张倩,李海洋. 稀疏信息处理中的迭代分式阈值算法[J]. 山东大学学报(理学版), 2017, 52(9): 76-82.
[2] 施章磊,李维国. A分级硬阈值追踪[J]. 山东大学学报(理学版), 2017, 52(8): 58-64.
[3] 潘文华,徐常青. 一类稀疏图的邻和可区别边色数[J]. 山东大学学报(理学版), 2017, 52(8): 94-99.
[4] 于文静,毕东旭,颜学峰. 基于结构自动匹配的仿射相似破损图像修复[J]. 山东大学学报(理学版), 2017, 52(3): 32-37.
[5] 崔静,梁秋菊. 分数布朗运动驱动的非局部随机积分微分系统的存在性与可控性[J]. 山东大学学报(理学版), 2017, 52(12): 81-88.
[6] 张琬迪,宋晓秋,吴尚伟. 一类模糊积分微分方程的模糊微分变换法[J]. 山东大学学报(理学版), 2017, 52(10): 42-49.
[7] 李双安,陈凤华,赵艳伟. 超记忆梯度法在大规模信号重构问题中的应用[J]. 山东大学学报(理学版), 2017, 52(1): 65-73.
[8] 王文淑,李维国,秦淑兰. 新的加速Bregman迭代方法在稀疏最小二乘问题中的应用[J]. 山东大学学报(理学版), 2016, 51(6): 92-98.
[9] 吴志勤1,石东伟2. 带弱奇异核非线性积分微分方程的收敛性分析[J]. J4, 2012, 47(8): 60-63.
[10] 李荣1,2. 三层一维非金属薄膜材料热传导效应的研究[J]. J4, 2012, 47(7): 39-43.
[11] 翟汝坤,蒋晓芸. 复杂人体组织传热的时间分数阶模型及其解[J]. J4, 2012, 47(6): 1-4.
[12] 邵伟1,祝丽萍2,刘福国2,王秋平2. 对称阵稀疏主成分分析及其在充分降维问题中的应用[J]. J4, 2012, 47(4): 116-120.
[13] 马云艳,栾贻会*. 基于局部LRS方法的稀疏信号片段检测[J]. J4, 2012, 47(12): 1-5.
[14] 黄玉娟1, 于文广2. 稀疏过程下保费与理赔相关的风险模型的破产概率[J]. J4, 2011, 46(7): 56-59.
[15] 雒金梅,左连翠*. 关于图的L(2,1)-标号的岛序列[J]. J4, 2011, 46(6): 49-52.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!