[1]孙宗岐,杨鹏.带投资和障碍分红的破产时刻Laplace变换[J].深圳大学学报理工版,2021,38(2):214-220.[doi:10.3724/SP.J.1249.2021.02214]
　SUN Zongqi and YANG Peng.The Laplace transform of ruin time with investment and barrier dividend[J].Journal of Shenzhen University Science and Engineering,2021,38(2):214-220.[doi:10.3724/SP.J.1249.2021.02214]
点击复制

带投资和障碍分红的破产时刻Laplace变换()
分享到：

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第38卷
期数:
2021年第2期
页码:
214-220
栏目:
数学与应用数学
出版日期:
2021-03-12

文章信息/Info

Title:
The Laplace transform of ruin time with investment and barrier dividend
文章编号:
202102015
作者:
孙宗岐1; 杨鹏2
1) 西京学院医学院，陕西西安 710123
2) 西京学院理学院，陕西西安 710123
Author(s):
SUN Zongqi1 and YANG Peng2
1) Medical College, Xijing University, Xi’an 710123, Shaanxi Province, P.R.China
2) College of Science, Xijing University, Xi’an 710123, Shaanxi Province, P.R.China
关键词:
运筹学; 对策论; 复合Poisson-Geometric过程; 风险投资; 障碍分红; Gerber-Shiu函数; 破产时刻Laplace变换
Keywords:
operations research;  game theory;  compound Poisson-Geometric process;  venture capital investment;  barrier dividend;  Gerber-Shiu function;  Laplace transform of ruin time
分类号:
O211.63
DOI:
10.3724/SP.J.1249.2021.02214
文献标志码:
A
摘要:
考虑复合Poisson-Geometric风险下带有投资和障碍分红的Gerber-Shiu函数问题，运用全期望公式得到复合Poisson-Geometric风险下带投资和障碍分红的Gerber-Shiu函数所满足的微分-积分方程．在指数分布假设下，得到带投资和障碍分红的保险公司破产时刻Laplace变换的显式解．
Abstract:
In order to study the Gerber-Shiu function for a compound Poisson-Geometric risk model with investment and barrier dividend, we obtain the differential-integral equation of the Gerber-Shiu function by using the method of total expectation formula. Under the assumption of exponential distribution, the explicit solution of the Laplace transform of ruin time of insurance company with investment and barrier dividend is given.

参考文献/References:

［1］ GERBER H, SHIU E. On the time value of ruin［J］. North America Actuarial Journal, 1998, 2(1): 48-72.
［2］ LIN X S, PAVLOVA K P. The compound Poisson risk model with a threshold dividend strategy［J］. Insurance: Mathematics and Economics, 2006, 38(1): 57-80.
［3］ 赵金娥,李明. 一类稀疏风险模型的Gerber-Shiu函数和最优红利策略［J］. 应用概率统计，2014，30(4)：439-448.
ZHAO Jin’e, LI Ming. On the Gerber-Shiu function and optimal dividend strategy for a thinning risk model［J］. Journal of Applied Probability and Statistics, 2014, 30(4): 439-448.(in Chinese)
［4］ 陈洁，吕玉华. 带分红的稀疏风险模型的期望折现罚金函数［J］. 山东大学学报理学版, 2015, 50(9): 78-83.
CHEN Jie, LV Yuhua. Discounted penalty function for a thinning risk model with dividend［J］. Journal of Shandong University Natural Science, 2015, 50(9): 78-83.(in Chinese)
［5］ 韩树新, 张兴宽. 两类带分红稀疏风险模型的期望折现罚金函数［J］. 南开大学学报自然科学版, 2016, 49(5): 92-101.
HAN Shuxin, ZHANG Xingkuan. The expected discounted penalty function of thing risk models with Barrier dividend［J］. Acta Scientiarum Naturalium Universitatis Nankaiensis, 2016, 49(5): 92-101.(in Chinese)
［6］ 毛泽春，刘锦萼. 一类索赔次数的回归模型及其在风险分级中的应用［J］. 应用概率统计，2004，20(4): 359-367.
MAO Zechun, LIU Jin’e. A regression model based on double parameters Poisson distribution and its applications to risk classification［J］. Chinese Journal of Applied Probability Statistics, 2004，20(4): 359-367.(in Chinese)
［7］ 贺丽娟，王成勇，张锴. 变保费率复合Poisson-Geometric 过程风险模型的Gerber-Shiu折现惩罚函数［J］.工程数学学报，2016，33(2): 121-130.
HE Lijuan, WANG Chengyong, ZHANG Kai. Gerber-Shiu discounted penalty function for compound Poisson-Geometric risk model with variable premium rate［J］. Chinese Journal of Engineering Mathematics ,2016，33(2): 121-130.(in Chinese)
［8］ 乔克林, 韩建勤. 改进后的复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数［J］. 系统科学与数学, 2016, 36(10): 1743-1752.
QIAO Kelin, HAN Jianqin. The Gerber-Shiu discounted penalty function of an improved Poisson-Geometric risk model［J］. Journal of System Science and Mathematics Science, 2016, 36(10): 1743-1752.(in Chinese)
［9］ YANG Long, DENG Guohe, YANG Li, et al. A perturbed risk model with dependence based on a generalized Farlie-Gumber-Morgenrstern copula［J］. Chinese Journal of Applied Probability and Statistics, 2019, 35(4): 373-396.(in Chinese)
［10］ 苏必超, 李婧超. 经典风险模型中破产变量的联合分布［J］. 深圳大学学报理工版，2019，36(4)：419-423.
SU Bichao, LI Jingchao. The joint distribution of ruin related quantities in the classical risk model［J］. Journal of Shenzhen University Science and Engineering, 2019, 36(10): 419-423.(in Chinese)
［11］ 孙宗岐，刘宣会，陈思源，等. 基于注资-有界分红的随机微分投资-再保博弈［J］. 深圳大学学报理工版，2017，33(4)：364-371.
SUN Zongqi, LIU Xuanhui, CHEN Siyuan, et al. Stochastic differential investment-reinsurance games with capital injection-barrier dividend［J］. Journal of Shenzhen University Science and Engineering, 2017, 33(4): 364-371.(in Chinese)
［12］ 孙宗岐，陈志平. 复合Poisson-Geometric风险下保险公司的最优投资-再保-混合分红策略［J］. 工程数学学报，2016，33(5)：463-479.
SUN Zongqi, CHEN Zhiping. Optimal investment-reinsurance-hybrid dividend strategies for insurance company under compound Poisson-Geometric risk process［J］. Journal of Engineering Mathematics, 2016, 33(5): 463-479.(in Chinese)
［13］ 汤珂. 随机过程与金融衍生品［M］. 北京:中国人民大学出版社, 2014.
TANG Ke. The stochastic process and financial derivatives［M］. Beijing: Renmin University of China Press, 2014.(in Chinese)

相似文献/References:

[1]马江山,李昱莹.基于卷积的自助银行选址分析[J].深圳大学学报理工版,2018,35(1):92.[doi:10.3724/SP.J.1249.2018.01092]
　MA Jiangshan and LI Yuying.Self-help bank location analysis based on convolution[J].Journal of Shenzhen University Science and Engineering,2018,35(2):92.[doi:10.3724/SP.J.1249.2018.01092]
[2]何基好,向淑文,贾文生,等.基于有限理性的信息集广义多目标博弈[J].深圳大学学报理工版,2018,35(1):105.[doi:10.3724/SP.J.1249.2018.01105]
　HE Jihao,XIANG Shuwen,et al.Information set generalized multi-objective games based on bounded rationality[J].Journal of Shenzhen University Science and Engineering,2018,35(2):105.[doi:10.3724/SP.J.1249.2018.01105]
[3]孙宗岐,刘宣会,陈思源,等.基于注资-有界分红的随机微分投资-再保博弈[J].深圳大学学报理工版,2017,34(4):364.[doi:10.3724/SP.J.1249.2017.04364]
　Sun Zongqi,Liu Xuanhui,Chen Siyuan,et al.Stochastic differential investment-reinsurance games with capital injection-barrier dividend[J].Journal of Shenzhen University Science and Engineering,2017,34(2):364.[doi:10.3724/SP.J.1249.2017.04364]

备注/Memo

备注/Memo:
Received：2020-01-04；Accepted：2020-03-02
Foundation：National Natural Science Foundation of China (71371152); Natural Science Foundation of Education Department of Shaanxi Province (2016JK2150 )
Corresponding author：Associate professor SUN Zongqi. E-mail: szqi200679@sina.com
Citation：SUN Zongqi, YANG Peng. The Laplace transform of ruin time with investment and barrier dividend［J］. Journal of Shenzhen University Science and Engineering, 2021, 38(2): 214-220.（in Chinese）
基金项目：国家自然科学基金资助项目（71371152）；陕西省教育厅自然科学专项基金资助项目 (2016JK2150)
作者简介：孙宗岐（1979—），西京学院副教授．研究方向：随机分析与运筹. E-mail: szqi200679@sina.com
引文：孙宗岐，杨鹏. 带投资和障碍分红的破产时刻Laplace变换［J］. 深圳大学学报理工版，2021，38(2)：214-220.
更新日期/Last Update: 2021-03-30