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 depende...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.展开更多
For the widely orthant dependent (WOD) structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tai...For the widely orthant dependent (WOD) structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tails. The obtained results extend some corresponding results.展开更多
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
In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to hav...In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV (extended regular variation). Lundberg type limiting results on the finite time ruin probabilities are also investigated.展开更多
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...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).展开更多
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
基金Supported by the National Natural Science Foundation of China(Nos.11571058&11301481)Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004)Fundamental Research Funds for the Central Universities(No.DUT17LK31)
文摘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.
文摘For the widely orthant dependent (WOD) structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tails. The obtained results extend some corresponding results.
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 National Natural Science Foundation of China(No.10971157)
文摘In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV (extended regular variation). Lundberg type limiting results on the finite time ruin probabilities are also investigated.
基金Research supported by National Science Foundation of China(No.10271087)
文摘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).
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.