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独立随机变量乘积的分布性状 被引量：2

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摘要 设X与Y为相互独立的非负随机变量,考察乘积XY的尾分布性状．可将X视为初始资本,而Y则是利率的影响．在现代金融保险业中,通常假定 X属于一定的分布族,而要考虑的问题是:Y的尾分布性状会对XY的尾性状产生怎样的影响?在怎样的条件下,XY能够保持X的原有族性?探讨了当X 的分布属于L族和S族时,XY的分布仍能属于相应分布族的条件,这些条件远远弱于既往文献中所给出的条件．同时还证明了:当X服从L(γ)(γ>0)族连续分布时,XY的分布属于C族的充要条件是Y为无界随机变量．
作者 苏淳 陈昱
机构地区 中国科学技术大学统计与金融系
出处 《中国科学（A辑）》 CSCD 北大核心 2006年第2期161-178,共18页 Science in China(Series A)
基金 国家自然科学基金(批准号:10371117) 教育部博士点基金 中国科学技术大学高水平大学建设基金资助项目
关键词 独立积 稳定性 尾分布 重尾
分类号 O211.5 [理学—概率论与数理统计] TP393 [自动化与计算机技术—计算机应用技术]
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参考文献9

  • 1Embrechts P,Klüppelberg C,Mikosch T.Modelling Extremal Events for Insurance and Finance.Berlin:Springer,1997
  • 2Tang Q,Tsitsiashvili G.Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks.Stochastic Processes and Their Applications,2003,108:299～325
  • 3Cline D B H,Samorodnitsky G.Subexponentiality of the product of independent random variables.Stochastic Process and Their Applications,1994,49:75～98
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  • 5Shimura T.The product of independent random variables with slowly varying truncated moments.J Austral Math Soc Ser A,1997,62:186～197
  • 6Su C,Chen J,Hu Z.Some discussions on the class L(γ).Journal of Mathematical Science,2004,122(4):3416～3425
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同被引文献11

  • 1王岳宝,成凤炀,杨洋.关于重尾分布间的控制关系及其应用[J].应用概率统计,2005,21(1):21-30. 被引量：11
  • 2EMBROCATES P, KLUPPELBERG C, MIKOSCH T. Modelling extreme events for insurance and finance [M]. Berlin: Springer, 1997.
  • 3CLINE D B H,SAMOROODNITSKY G. Subexponentiality of the product of independent random variables [J]. Stochastic Process and Their Applications, 1994,49 : 75-98.
  • 4SHIMURA T. The product of independent random variables with slowly varying truncated moments [J]. Journal of the Australian Mathematical Society, 1997,62:186-197.
  • 5CAI J,TANG Q. On maxisum equivalence and convolution closure of heavy-tailed distributions and their applications [J]. Journal of Applied Probability, 2004,41 : 117-130.
  • 6EMBRECHTS P, GOLDIE C. On closure and faetorization properties of sub-exponential and related distributions [J]. Journal of the Australian Mathematical Society, 1980,29; 243- 256.
  • 7TANG Q,TSITSIASHVILI G. Precise estimates for the ruinprobability infinite horizonina discrete-time model with heavytailed insurance and financial risks [J]. Stochastic Process and There Application, 2003,108(2) : 299-325.
  • 8TOMASZ R,TEUGELS J M. Stochestic process for insurance and finance [M]. New York:Johe wiley, 1999.
  • 9Embrechts P,Klüppelberg C,Mikosch T.Modelling extremal events for insurance and finance[M].Berlin:Springer,1997:36-57.
  • 10Su Chun,Chen Jing,Hu Zhishui.Some discussions on the class L(γ)[J].Journal of Mathematical Sciences,2004,122(4):3416-3425.

引证文献2

二级引证文献6

中国科学（A辑）
2006年 第2期

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