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Precise Large Deviations for Sums of Negatively Associated Random Variables with Common dominatedly varying tails

Acta Mathematica Sinica,English Series 2006年第6期22卷 1725-1734页

作者： Yue Bao WANG Kai Yong WANG Dong Ya CHENG School of Mathematics Science Soochow University Suzhou 215006 P. R. China Department of Applied Mathematics University of Science and Technology of Suzhou Suzhou 215009 P. R. China

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）.

关键词： negatively associated dominatedly varying tail precise large deviation

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Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

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Applied Mathematics(A Journal of Chinese Universities) 2015年第3期30卷 347-360页

作者： FU Ke-ang QIU Yu-yang WANG An-ding School of Statistics and Mathematics Zhejiang Gongshang University

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

关键词： by-claim dominatedly varying tail extended upper negative dependence quasi-asymptotic independence ruin probability time-depende

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Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

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Journal of Southeast University(English Edition) 2014年第1期30卷 118-121页

作者：杨洋刘伟林金官张玉林东南大学经济管理学院南京210096 南京审计学院数学与统计学院南京210029 新疆大学数学与系统科学学院乌鲁木齐830046 东南大学数学系南京210096

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

关键词： compound and non-compound risk models finite-time ruin probability dominatedly varying tail uniformasymptotics random sums dependence structure

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