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变保费率的扰动多险种模型总索赔盈余的大偏差 被引量：1

Large Deviations of the Surplus of Aggregate Claims for a Perturbed Multi-risk Model with Variable Premium Rate
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摘要 考虑变保费率的扰动多险种更新模型.在索赔额分布属于一致变化类的条件下,给出总索赔盈余过程的精致大偏差. In this paper, the perturbed multi-risk renewal model is considered. When the claim-size distributions belong to the consistent variation class, we present the precise large deviation for the surplus process of aggregate claims.
作者 董英华 罗琦
机构地区 南京信息工程大学数理学院 南京信息工程大学信息与控制学院
出处 《数学的实践与认识》 CSCD 北大核心 2011年第23期10-17,共8页 Mathematics in Practice and Theory
基金 国家自然科学基金(61174077)
关键词 多险种模型 变保费率 布朗运动 更新模型 精致大偏差 multi-risk model variable premium rate Brownian motion renewal model precise large deviation
分类号 F224 [经济管理—国民经济] F840 [经济管理—保险]
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参考文献14

  • 1Dufresne F, Gerber H U. Risk theory for the compound Poisson process that is perturbed by diffusion[J]. Insurance: Mathematics and Economics. 1991, 10: 51-59.
  • 2Schlegel S. Ruin probabilities in perturbed risk models[J]. Insurance: Mathematics and Economics. 1998, 22: 93-104.
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  • 7Tang Qihe, Su Chun, Jiang Tao, Zhang Jinsong. Large deviations for heavy-tailed random sums in compound renewal model[J]. Statistics and Probability Letters. 2001, 52: 91-100.
  • 8Ng Kai W, Tang Qihe, Yan Jiaan, Yang Hailiang. Precise large deviations for sums of random variables with consistently varying tails[J]. Journal of Applied Probability. 2004, 40: 391-400.
  • 9韦晓,于金酉,胡亦钧.变保费率扰动风险模型的有限时间破产概率和大偏差[J].数学物理学报（A辑）,2007,27(4):616-623. 被引量：3
  • 10Wang Shijie, Wang, Wensheng. Precise large deviations for sums of random variables with consis- tently varying tails in multi-risk models[J]. Journal of Applied Probability. 2007, 44: 889-900.

二级参考文献17

  • 1Asmussen S.Ruin Probabilities.Singapore:World Scientific,2000.
  • 2Gerber H U.An introduction of the renewed equation and its application in the collective theory of risk.Skand Aktuar Tidskr,1970,205-210.
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  • 8Schlegel S.Ruin probabilities in perturbed risk models.Insurance:Mathematics and Economics,1998,22:93-104.
  • 9Wang G,Wu R.Some distributions forclassical risk processes that is perturbed by diffusion.Insurance:Mathematics and Econoimic,2000,26:15-24.
  • 10Schmidli H.Distribution of the first ladder height of a stationary risk process perturbed by α-stable Lévy motion.Insurance:Mathematics and Economic,2001,28:13-20.

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数学的实践与认识
2011年 第23期

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