| 多重延迟的关键更新定理及其在风险理论中的应用 |
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| 引用本文： | 王开永,林金官,杨洋.多重延迟的关键更新定理及其在风险理论中的应用[J].数学年刊A辑(中文版),2015,36(2):217-232. |
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| 作者姓名： | 王开永 林金官 杨洋 |
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| 作者单位： | 苏州科技学院数理学院, 江苏 苏州 215009; 东南大学数学系, 南京 210096.,东南大学数学系, 南京 210096.,南京审计学院理学院, 南京 210029. |
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| 基金项目： | 本文受到国家自然科学基金 (No.11401418, No.11171065, No.71471090), 国家自然科学基金数学天元基金(No.11226211),
中国博士后基金(No.2012M520963) 和江苏省自然科学基金(No.BK2012165)的资助. |
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| 摘 要： | 利用广义局部次指数分布族的性质,讨论了带有多重延迟且Lundberg指数不存在时的关键更新定理,所得结果包含了重尾和轻尾的情形.将此结果应用到平稳更新风险模型,得到了该模型在破产时亏损额分布的局部渐近性质.
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| 关 键 词： | 广义局部次指数分布族 关键更新定理 多重延迟 平稳更新风险模型 |
The Key Renewal Theorem with Multi-delay and
Applications to Risk Theory |
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| WANG Kaiyong,LIN Jinguan and YANG Yang.The Key Renewal Theorem with Multi-delay and
Applications to Risk Theory[J].Chinese Annals of Mathematics,2015,36(2):217-232. |
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| Authors: | WANG Kaiyong LIN Jinguan and YANG Yang |
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| Institution: | Corresponding author. School of Mathematics and Physics, Suzhou University
of Science and Technology, Suzhou 215009, Jiangsu, China; Department of
Mathematics, Southeast University, Nanjing 210096, China.Department of Mathematics, Southeast University, Nanjing 210096, China.College of Science, Nanjing Audit University, Nanjing 210029, China. |
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| Abstract: | Using the properties of the extensively local subexponential distribution class,
the authors investigate the key renewal theorem with multi-delay and without the Lundberg
exponent. The obtained results contain the heavy-tailed and light-tailed cases. Applying
the results to the stationary renewal risk model, the local asymptotics for the distribution
of the deficit at ruin are obtained. |
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| Keywords: | Extensively local subexponential distributions Key renewal theorem Multi-delay Stationary renewal risk model |
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