共查询到10条相似文献,搜索用时 125 毫秒
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We investigate the precise large deviations of random sums of negatively dependent random variables with consistently varying tails. We find out the asymptotic behavior of precise large deviations of random sums is insensitive to the negative dependence. We also consider the generalized dependent compound renewal risk model with consistent variation, which including premium process and claim process, and obtain the asymptotic behavior of the tail probabilities of the claim surplus process. 相似文献
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We investigate precise large deviations for heavy-tailed random sums. We prove a general asymptotic relation in the compound
renewal risk model for consistently varying-tailed distributions. This model was introduced in [Q. Tang, C. Su, T. Jiang,
and J.S. Zang, Large deviation for heavy-tailed random sums in compound renewal model, Stat. Probab. Lett., 52:91–100, 2001] as a more practical risk model. The proof is based on the inequality found in [D. Fuk and S.V. Nagaev,
Probability for sums of independent random variables, Theory Probab. Appl., 16:600–675, 1971]. 相似文献
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Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation 总被引:5,自引:0,他引:5
The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend
recent results of Tang (Electron J Probab 11(4):107–120, 2006) and Liu (Stat Probab Lett 79(9):1290–1298, 2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal
risk model in which innovations, modelled as real-valued random variables, are negatively dependent with common consistently-varying-tailed
distribution, and their inter-arrival times are also negatively dependent. 相似文献
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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. 相似文献
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Fotis Loukissas 《Journal of Theoretical Probability》2012,25(4):913-924
In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes. 相似文献
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Georgios Psarrakos 《Insurance: Mathematics and Economics》2010,47(3):428-433
In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution. 相似文献
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Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails 总被引:1,自引:0,他引:1
Yue Bao WANG Kai Yong WANG Dong Ya CHENG 《数学学报(英文版)》2006,22(6):1725-1734
In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang (J. Appl. Prob., 41, 93-107, 2004). 相似文献
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本文考虑了索赔时间间距为广义Erlang(n)分布的带干扰更新(Sparre Andersen)风险过程.所用的方法类似于Albrecher,et al.(2005),即将广义Erlang(n)随机变量分解成n个独立的指数随机变量的和.建立了破产前最大盈余所满足的积分-微分方程,讨论了索赔量分布为K<,m>分布时的特殊情形. 相似文献