Large deviations for random sums of differences between two sequences of random variables with applications to risk theory

Yang Yang; Jie Liu; Yuquan Cang

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Large deviations for random sums of differences between two sequences of random variables with applications to risk theory

机译：两个随机变量序列之间的差之和的随机和的大偏差，并应用于风险理论

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This paper investigates some precise large deviations for the random sums of the differences between two sequences of independent and identically distributed random variables, where the minuend random variables have subexponential tails, and the subtrahend random variables have finite second moments. As applications to risk theory, the customer-arrival-based insurance risk model is considered, and some uniform asymptotics for the ruin probabilities of an insurance company are derived as the number of customers or the time tends to infinity. MSC:60F10, 62E20, 62P05.

机译：本文研究了独立且均匀分布的两个随机变量序列之间的差之和的精确精确大偏差，其中，最小随机变量具有次指数尾部，而次级随机变量具有有限的第二矩。作为风险理论的应用，考虑了基于客户到达的保险风险模型，并且随着客户数量或时间趋于无穷大，得出了保险公司破产概率的一些统一渐近性。 MSC：60F10、62E20、62P05。

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《Journal of inequalities and applications》 |2012年第1期|共9页
作者
Yang Yang; Jie Liu; Yuquan Cang;
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1. Large deviations for random sums of differences between two sequences of random variables with applications to risk theory [J] . Yang Yang, Jie Liu, Yuquan Cang Journal of inequalities and applications . 2012,第1期

机译：两个随机变量序列之间的差之和的随机和的大偏差，并应用于风险理论
2. Large deviations for random sums of differences between two sequences of random variables with applications to risk theory [J] . Yang Yang, Jie Liu, Yuquan Cang Journal of inequalities and applications . 2012,第1期

机译：两个随机变量序列之间的差之和的随机和的大偏差，并应用于风险理论
3. Large deviations for random sums of differences between two sequences of random variables with applications to risk theory [J] . Yang Yang, Jie Liu, Yuquan Cang Journal of inequalities and applications . 2012,第1期

机译：两个随机变量序列之间的差之和的随机和的大偏差，并应用于风险理论
4. A class of random deviation theorems for weighted sums of continuous random variables [C] . Yuesheng Song, Weiguo Yang 2009 International Workshop on Information Security and Application(2009 信息安全与应用国际研讨会） . 2009

机译：连续随机变量加权和的一类随机偏差定理
5. Small deviations of sums of random variables. [D] . Garnett, Brian. 2016

机译：随机变量总和的小偏差。
6. Complete convergence and complete moment convergence for randomly weighted sums of martingale difference sequence [O] . Huanhuan Ma, Yan Sun -1

机译：mar差序列随机加权和的完全收敛和完全矩收敛
7. Large deviations for random sums of differences between two sequences of random variables with applications to risk theory [O] . Yang Yang, Jie Liu, Yuquan Cang 2012

机译：两个随机变量序列之间的差之和的随机和的大偏差，并应用于风险理论
8. Large and Moderate Deviation Limit Theorems for Arbitrary Sequences of Random Variables, with Applications. [R] . Chaganty, N. R. 1991

机译：随机变量任意序列的大中偏差定理及其应用。

Large deviations for random sums of differences between two sequences of random variables with applications to risk theory

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