DOI: 10.3724/SP.J.1160.2013.00345

Acta Analysis Functionalis Applicata (应用泛函分析学报) 2013/15:4 PP.345-348

Precise Large Deviations for Sums of Widely Upper Orthant Dependent Random Variables

This paper investigates the precise large deviation for widely upper orthant dependent random variables with long tailed distributions,and obtains the asymptotic relations for both the partial suns and the random sums by using the classic method of large deviation.

Key words:precise large deviation,long tailed distribution,widely upper orthant dependence

ReleaseDate:2015-04-21 14:22:09

1 孙立娟,顾岚. 保险公司破产概率的估计及随机模拟[J].系统工程理论与实践,2000,(07):63-68.

2 Sun L J,Gu L. An estimate and stochastic simulation of the ruin probability for an insurance company[J].Systems Engineering-Theory & Practice,2000,(07):63-68.

3 高健伟,邱菀华. 定期人寿保险中的破产概率[J].系统工程理论与实践,2002,(05):66-70.

4 Gao J W,Qiu W H. Ruin model of term life insurance[J].Systems EngineeringTheory & Practice,2002,(05):66-70.

5 张未未,赵选民,李艳玲. 两类相关索赔模型下破产概率的若干结果[J].系统工程理论与实践,2005,(01):43-48.

6 Zhang W W,Zhao X M,Li Y L. Some results of ruin probabilities in a correlated claims model[J].Systems Engineering-Theory & Practice,2005,(01):43-48.

7 林祥. 关于“定期人寿保险中的破产概率”的注记[J].系统工程理论与实践,2005,(04):141-144.

8 Lin X. A note to ruin model of term life insurance[J].Systems Engineering-Theory & Practice,2005,(04):141-144.

9 Tang Q H,Su C,Jiang T. Large deviations for heavy-tailed random sums in compound renewal model[J].Statistics & Probability Letters,2001.91-100.

10 Ng K W,Tang Q H,Yan J A. Precise large deviation for sums of random variables with consistently varying tails[J].Journal of Applied Probability,2004.93-107.

11 Fotis L. Precise large deviations for long-tailed distributions[J].Journal of Theoretical Probability,2012.913-107.

12 汪世界. 带一致变化尾上负相关随机变量和的精确大偏差[J].合肥工业大学学报(自然科学版),2010,(03):464-466.doi:10.3969/j.issn.1003-5060.2010.03.033.

13 Wang S J. Precise large deviations for sums of upper negatively dependent random variables with consistently varying tails[J].Journal of Hefei University of Technology,2010,(03):464-466.doi:10.3969/j.issn.1003-5060.2010.03.033.

14 Li L. Precise large deviation for dependent random variables with heavy tails[J].Statistics & Probability Letters,2009.1290-1298.

15 Wang Y B,Cui Z L,Wang K Y. Uniform asymptotic of the finite-time ruin probability for all times[J].Journal of Mathematical Analysis and Applications,2012.208-223.