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Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate 被引量:1
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作者 杨洋 刘伟 +1 位作者 林金官 张玉林 《Journal of Southeast University(English Edition)》 EI CAS 2014年第1期118-121,共4页
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 cla... 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. 展开更多
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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D族END的随机变量和的精确大偏差 被引量:1
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作者 华志强 董莹 玄海燕 《应用泛函分析学报》 2015年第1期66-70,共5页
研究了非随机和的S_n=∑_(i=1)~n X_i,n≥1的精确大偏差的问题,这里{X_i,i≥1}是服从控制变化尾分布族(D族)的非负的、END的随机变量,但不必是同分布的.在给定的一些假设条件下,得到了非随机和的渐近关系,推广了相应的独立同分布情... 研究了非随机和的S_n=∑_(i=1)~n X_i,n≥1的精确大偏差的问题,这里{X_i,i≥1}是服从控制变化尾分布族(D族)的非负的、END的随机变量,但不必是同分布的.在给定的一些假设条件下,得到了非随机和的渐近关系,推广了相应的独立同分布情形下的结论. 展开更多
关键词 控制变化尾 延拓负相依 精确大偏差
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D族END随机变量的随机和的精确大偏差 被引量:2
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作者 华志强 《应用泛函分析学报》 2015年第4期354-360,共7页
设{X_i,i≥1}是一列服从控制变化尾分布族(D族)的非负的、END的但不必是同分布的随机变量序列,{N_t,t≥0}是一列取非负正整数值的随机变量序列.在给定一些假设条件下,得到了随机和的S(t)=∑_(i=1)^(N(t))X_i(t≥0)的精确大偏差的结论,... 设{X_i,i≥1}是一列服从控制变化尾分布族(D族)的非负的、END的但不必是同分布的随机变量序列,{N_t,t≥0}是一列取非负正整数值的随机变量序列.在给定一些假设条件下,得到了随机和的S(t)=∑_(i=1)^(N(t))X_i(t≥0)的精确大偏差的结论,推广了独立情形下的相应结论. 展开更多
关键词 延拓负相依 精确大偏差 控制变化尾 随机和
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D族相依理赔下依时更新风险模型破产概率的渐近估计 被引量:1
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作者 裘渔洋 李杰 傅可昂 《高校应用数学学报(A辑)》 CSCD 北大核心 2013年第3期277-286,共10页
考虑一非标准更新风险模型,其中理赔额与其等待时间构成一个同分布的非负随机向量序列,且每个随机向量内部具有某种相依结构.在理赔额为上尾独立的D族随机变量的假定下,建立了盈余过程有限时和无限时破产概率的渐近估计.
关键词 控制变化尾 上尾独立 依时更新风险模型 破产概率
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A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails 被引量:20
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作者 唐启鹤 严加安 《Science China Mathematics》 SCIE 2002年第8期1006-1011,共6页
Let F be a distribution function supported on (-∞,∞) with a finite mean μ. In this note we show that if its tail F = 1 - F is dominatedly varying, then for any r > max{μ, 0}, there exist C(r) > 0 and D(r) &g... Let F be a distribution function supported on (-∞,∞) with a finite mean μ. In this note we show that if its tail F = 1 - F is dominatedly varying, then for any r > max{μ, 0}, there exist C(r) > 0 and D(r) > 0 such thatfor all n ≥ 1 and all x≥rn. This inequality sharpens a classical inequality for the subexponential distribution case. 展开更多
关键词 dominatedly VARYING tails subexponential distribution tail probabilities.
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Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails 被引量:19
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作者 Yue Bao WANG Kai Yong WANG Dong Ya CHENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第6期1725-1734,共10页
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
关键词 negatively associated dominatedly varying tail precise large deviation
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Precise large deviations for widely orthant dependent random variables with dominatedly varying tails 被引量:15
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作者 Kaiyong WANG Yang YANG Jinguan LIN 《Frontiers of Mathematics in China》 SCIE CSCD 2012年第5期919-932,共14页
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
关键词 Precise large deviations widely orthant dependent (WOD) dominatedly varying tails
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Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims 被引量:2
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作者 FU Ke-ang QIU Yu-yang WANG An-ding 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第3期347-360,共14页
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... 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. 展开更多
关键词 by-claim dominatedly varying tail extended upper negative dependence quasi-asymptotic independence ruin probability time-depende
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THE STRUCTURE AND PRECISE MODERATE DEVIATIONS OF RANDOM VARIABLES WITH DOMINATEDLY VARYING TAILS 被引量:3
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作者 WANGYuebao YANGYang 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第2期224-232,共9页
This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random c... This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random centralizing constants, which extend the boundary γλ(t)of large deviations to γ(λ(t)^1/s,whereγ>0,1<s<2,λ(t)is the expectation of the random index N(t),t>0. 展开更多
关键词 STRUCTURE precise moderate deviations dominatedly varying tails
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D族分布下带投资的双险种风险模型中的破产概率
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作者 王施施 王文胜 骆明旭 《杭州师范大学学报(自然科学版)》 CAS 2017年第1期94-102,共9页
研究了带投资的双险种更新风险模型中的破产概率.该模型中允许保险公司将其部分盈余投资于满足几何布朗运动的Black-Scholes型资本市场,对此模型假定同一险种索赔额是两两拟渐近独立的,根据Ito公式得到公司盈余过程的表达式,基于该模型... 研究了带投资的双险种更新风险模型中的破产概率.该模型中允许保险公司将其部分盈余投资于满足几何布朗运动的Black-Scholes型资本市场,对此模型假定同一险种索赔额是两两拟渐近独立的,根据Ito公式得到公司盈余过程的表达式,基于该模型分析了当索赔额满足D族分布时破产概率渐近关系式,并由D族分布推出C族分布下破产概率的渐近关系式. 展开更多
关键词 破产概率 两两拟渐进独立 D族分布 C族分布 双险种风险模型
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RUIN PROBABILITIES WITH PAIRWISE QUASI-ASYMPTOTICALLY INDEPENDENT AND DOMINATEDLY-VARYING TAILED CLAIMS 被引量:1
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作者 Yinghua DONG Yuebao WANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第2期303-314,共12页
This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of... This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented. 展开更多
关键词 dominatedly varying tails nonstandard renewal risk model pairwise quasi-asymptotic independence perturbed renewal risk model weighted renewal function.
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△族中大偏差的一个不等式
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作者 曹晓敏 高珊 《经济数学》 2005年第2期202-207,共6页
在文献[2]中,F是一有有限期望μ支撑在(-∞,+∞)上的分布函数(d.f.).若其尾分布F=1-F属于D族,那么对任意的γ>max(μ,0),存在常数C(γ,0),存在常数C(γ)>0和D(γ)>0使得C(γ)nF(x)Fn*(x)D(γ)nF(x),对所有的n1和所有的x... 在文献[2]中,F是一有有限期望μ支撑在(-∞,+∞)上的分布函数(d.f.).若其尾分布F=1-F属于D族,那么对任意的γ>max(μ,0),存在常数C(γ,0),存在常数C(γ)>0和D(γ)>0使得C(γ)nF(x)Fn*(x)D(γ)nF(x),对所有的n1和所有的xγn成立.本文中我们将其推广成离散情况下精细大偏差的一个不等式,并进一步在连续时间下得到关于部分和S(t)=∑N(t)i=1Xi,t0的精细大偏差类似的不等式. 展开更多
关键词 控制变化尾 精细大偏差 不等式 大偏差 分布函数 F(X) 连续时间 尾分布 NCO 部分和
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The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks
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作者 YANG Yang LIN Jin-guan TAN Zhong-quan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第2期194-204,共11页
Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {(Xi, Yi), i≥1) form a seq... Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {(Xi, Yi), i≥1) form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability. 展开更多
关键词 ASYMPTOTICS long-tailed and dominatedly-varying-tailed distribution financial and insurancerisks finite-time ruin probability bivariate Sarmanov distribution.
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广义负相依重尾随机变量和及其最大值尾概率的渐近性
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作者 张婷 李峰 +1 位作者 杨洋 林金官 《应用概率统计》 CSCD 北大核心 2019年第1期39-50,共12页
假设X_1,X_2…,X_n是一列具有广义负相依结构的随机变量(r.v.s.),分别具有分布F_1,F_2,...,F_n.假设S_n:=X_1+X_2+…+X_n.本文分别在三类重尾分布族下得到了如下量之间的渐近关系:P(S_n>x),P(max{X_1,X_2,…,x_n}>x), P(max{S_1, ... 假设X_1,X_2…,X_n是一列具有广义负相依结构的随机变量(r.v.s.),分别具有分布F_1,F_2,...,F_n.假设S_n:=X_1+X_2+…+X_n.本文分别在三类重尾分布族下得到了如下量之间的渐近关系:P(S_n>x),P(max{X_1,X_2,…,x_n}>x), P(max{S_1, S_2,…,S_n}> X)和(?)P(X_k> x).在此基础上,本文还探讨了随机加权和最大值尾概率的渐近性质,并运用蒙特卡洛(CMC)数值模拟验证了其有效性.最后,本文将得到的主要结果应用到了一个带有保险风险与金融风险的离散时间风险模型,得到了有限时间破产概率的渐近性. 展开更多
关键词 广义负相依 一致变换尾分布 控制变换尾分布 长尾分布 蒙特卡洛模拟 离散时间风险模型 有限时间破产概率
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