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Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

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Applied Mathematics(A Journal of Chinese Universities) 2018年第4期33卷 491-502页

作者： SHEN Xin-mei FU Ke-ang ZHONG Xue-ting School of Mathematical Sciences Dalian University of Technology School of Statistics and Mathematics Zhejiang Gongshang University

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

关键词： Precise large deviation Size-dependent Consistent variation Multidimensional risk model renewal counting process

Precise large deviation result for heavy-tailed random sums and applications to risk theory

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Journal of Southeast University(English Edition) 2010年第3期26卷 498-501页

作者：杨洋林金官东南大学数学系南京211189 南京审计学院数学与统计学院南京210029

The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.

关键词： precise large deviation random sum sub-exponential distribution renewal counting process customer-arrival-based insurance risk model

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

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Chinese Quarterly Journal of Mathematics 2006年第1期21卷 71-79页

作者： KONG Fan-chao WANG Jin-liang Department of Mathematics Anhui University Hefei 230039 China

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and F... 详细信息

关键词： renewal risk model heavy-tailed distribution large deviation renewal counting process

Large Deviations for a Generalized Compound renewal Risk Model

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Chinese Quarterly Journal of Mathematics 2010年第3期25卷 399-406页

作者： GA O Shan School of Mathematics and Computational Science Fuyang Normal College Fuyang 236032 China

This paper extends the ordinary renewal risk model to the case where the premium income process,based on a renewal counting process,is no longer a linear function;and the total claim amount process is described by a c... 详细信息

关键词： heavy-tailed distribution renewal counting process large deviation