Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying...Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X1 are allowed to be generally dependent. Moreover, let N（.） be a nonnegative integer-valued process, independent of the sequence {Xi, i ≥ 1}. Under several mild assumptions, precise large deviations for Sn =∑i=1 n Xi and SN（t） =∑i=1 N（t） Xi are investigated. Meanwhile, some simulation examples are also given to illustrate the results.展开更多
Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
In this paper, we study the precise large deviations for the prospectiveloss process with consistently varying tails. The obtained results improve some related known ones.
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 in...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.展开更多
文摘Let {Xi = （X1,i,...,Xm,i）T, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X1 are allowed to be generally dependent. Moreover, let N（.） be a nonnegative integer-valued process, independent of the sequence {Xi, i ≥ 1}. Under several mild assumptions, precise large deviations for Sn =∑i=1 n Xi and SN（t） =∑i=1 N（t） Xi are investigated. Meanwhile, some simulation examples are also given to illustrate the results.
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
文摘In this paper, we study the precise large deviations for the prospectiveloss process with consistently varying tails. The obtained results improve some related known ones.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171321, 11271347） and the Fundamental Research Funds for the Central Universities.
文摘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.
