| 杨洋,林金官,王定成.宽象限相依随机变量部分和的中偏差及其在
保险中的应用*[J].数学年刊A辑,2015,36(4):375~388 |
| 宽象限相依随机变量部分和的中偏差及其在
保险中的应用* |
| Moderate Deviations for the Partial Sum of WidelyOrthant Dependent Random Variables andTheir Applications in Insurance |
| |
| DOI： |
| 中文关键词: 中偏差, 宽象限相依, 控制变换, 基于顾客到达过程的保险风险模型, 复合更新风险模 |
| 英文关键词:Moderate deviations,Widely orthant dependence, Dominated vari-
ation, Customer-arrival-based insurance risk model, Compound re-
newal risk model |
| 基金项目:本文受到国家自然科学基金 (No.71471090, No.71271042), 教育部人文社会科学研究青年基金 (No.14 YJCZH182),
中国博士后科学基金 (No.2014T70449, No.2012M520964), 江苏省自然科学基金 (No.BK 20131339), 江苏省高校自然科学基金重大项目(No.15KJA110001),
江苏省青蓝工程, 江苏省高校优秀科技创新团队项目, 江苏高校优势学科建设工程, 江苏省高校金融工程重点实验室和江苏省十二五重点建设学科 (统计学) 项目的资助. |
| Author Name | Affiliation | E-mail | | YANG Yang | Corresponding author. The Key Lab of Financial Engineering of Jiangsu
Province, Nanjing Audit University, Nanjing 211815, China
School of Eco-
nomics and Management, Southeast University, Nanjing 210096, China. | yyang@nau.edu.cn; yyangmath@gmail.com | | LIN Jinguan | Department of Mathematics, Southeast University, Nanjing 210096, China. | jglin@seu.edu.cn | | WANG Dingcheng | The Key Lab of Financial Engineering of Jiangsu Province, Nanjing Audit
University, Nanjing 211815, China. | wangdc@nau.edu.cn |
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| 中文摘要: |
| 研究了控制变换尾分布的宽象限相依实值随机变量部分和的中偏差.
相应于所得到的理论结果, 进一步给出了在相依保险风险模型中的两个应用:
一是在基于顾客到达过程的保险风险模型中, 保险公司盈余的渐近估计;
二是在复合更新风险模型中, 有限时和无限时破产概率的一致渐近估计. |
| 英文摘要: |
| This paper deals with the moderate deviations for the partial sum of widely
orthant dependent real-valued random variables with dominatedly varying tails. As an
illustration of the obtained results the authors give two applications related to some de-
pendent insurance risk models: The surplus of an insurance company is estimated in the
customer-arrival-based insurance risk model; and the uniform asymptotics for the finite-time
and infinite-time ruin probabilities are derived in the compound renewal risk model. |
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