复合更新风险模型中负相依索赔额下的精细大偏差（英文）

本文考虑了在复合更新风险模型当中,负相依索赔额情形下与之相关的精细大偏差的若干问题.文中假设{X_n,n≥1}是一列负相依的随机变量,其对应分布列为{F_n,n≥1},并假定F_n的右尾分布等同于某个具有一致变化尾的分布.根据所得的结果试图建立与经典大偏差相似的结论,并将其应用到改进后的复合更新风险模型当中.     

风险模型中重尾随机变量和的若干大偏差结果

进一步研究随机变量部分和与随机和的大偏差,其中S(n)=∑ni=1Xi,S(t)=∑N(t)i=1Xi(t>0).{Xn,n≥1}是一个独立同分布的随机变量(未必是非负的)序列具有共同的分布F(定义于R上)和有限期望μ=EX1.{N(t),t≥0}是一个非负的整数值的随机变量的更新计数过程且与{Xn,n≥1}相互独立.本文在假定F∈C条件下,进一步推广并改进了由Klüppelberg等和Kaiw等人给出的一些大偏差结果.这些结果可应用到某些金融保险方面的一些特定的问题中去.     

对于复合更新模型重尾随机和的大偏差结果的一个改进

本文在一个相对较弱的假设之下，得到了复合更新风险模型中重尾随机和的精确大偏差等价式，该结果对文[1]中的结果进行了改进。     

上尾渐近独立随机变量和的大偏差的渐近下界(英文)

本文研究了多元风险模型中服从长尾分布的带上尾渐近独立的随机变量和的大偏差渐近下界.利用大偏差的经典求法,得到了随机变量的非随机和和随机和的大偏差表达式,推广了独立同分布情形下的相关结论.     

变保费率的扰动多险种模型总索赔盈余的大偏差

考虑变保费率的扰动多险种更新模型.在索赔额分布属于一致变化类的条件下,给出总索赔盈余过程的精致大偏差.     

离散时多元风险模型的破产概率

本文研究了离散时多元风险模型的破产概率问题.利用经典大偏差的方法,获得了有限水平的破产概率,推广了离散时一元风险模型的相应结论.     

离散时多元风险模型的破产概率

本文研究了离散时多元风险模型的破产概率问题. 利用经典大偏差的方法, 获得了有限水平的破产概率, 推广了离散时一元风险模型的相应结论.     

一类新风险过程的精细大偏差

本文针对基于进入过程的保险风险模型(LIG),讨论了当索赔额属于C族时,风险过程的精细大偏差.     

变保费率扰动风险模型的有限时间破产概率和大偏差

该文考虑变保费率的扰动风险模型, 其中索赔的分布是重尾的. 对这个风险模型, 给出了索赔剩余过程的精细大偏差; 同时, 还得到了它的有限时间破产概率的Cramer-Lundberg型极限结果.     

L族END的多元部分和的精确大偏差下界

从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界.     

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??In this paper, precise large deviations of nonnegative, non-identical distributions and negatively associated random variables are investigated. Under certain conditions, the lower bound of the precise large deviations for the non-random sum is solved and the uniformly asymptotic results for the corresponding random sum are obtained. At the same time, we deeply discussed the compound renewal risk model, in which we found that the compound renewal risk model can be equivalent to renewal risk model under certain conditions. The relative research results of precise large deviations are applied to the more practical compound renewal risk model, and the theoretical and practical values are verified. In addition, this paper also shows that the impact of this dependency relationship between random variables to precise large deviations of the final result is not significant.     

Precise large deviations for a customer-based individual risk model

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 prospective-loss 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.     

负相协D族广义Sparre-Andevsen模型下的大偏差及其应用

本文将经典的Sparre-Andevsen风险模型推广到保费收入过程不再是线性过程的一般风险过程,得到了一些关于负相协D族随机变量随机和的大偏差结果,以及破产概率的弱等价性.     

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本文给出了带随机重延迟的大额索赔更新风险模型的局部破产概率的渐近表达式, 它与 原更新风险模型相应的局部破产概率的渐近表达式一致     

Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation

The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (Electron J Probab 11(4):107–120, 2006) and Liu (Stat Probab Lett 79(9):1290–1298, 2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued random variables, are negatively dependent with common consistently-varying-tailed distribution, and their inter-arrival times are also negatively dependent.     

Precise large deviations for generalized dependent compound renewal risk model with consistent variation

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.     

Asymptotic results for conditional measures of association of a random sum

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution.     

Precise large deviations for consistently varying-tailed distributions in the compound renewal risk model

We investigate precise large deviations for heavy-tailed random sums. We prove a general asymptotic relation in the compound renewal risk model for consistently varying-tailed distributions. This model was introduced in [Q. Tang, C. Su, T. Jiang, and J.S. Zang, Large deviation for heavy-tailed random sums in compound renewal model, Stat. Probab. Lett., 52:91–100, 2001] as a more practical risk model. The proof is based on the inequality found in [D. Fuk and S.V. Nagaev, Probability for sums of independent random variables, Theory Probab. Appl., 16:600–675, 1971].     

考虑背景风险的高阶矩三角模糊随机投资组合模型

在已有的大部分投资组合模型中,证券的收益服从随机分布或者模糊分布。然而,在实际的市场中存在大量的不确定性,市场不仅具有内在的风险,也存在由投资者个体差异产生的背景风险。本文推导随机模糊数的高阶矩性质,构建一个考虑背景风险的高矩三角模糊随机投资组合风险模型,采用沪深股市的数据分析背景风险对投资组合的影响。     

The Burgers equation with a random force and a general model for directed polymers in random environments

Summary. The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers equations. Received: 18 July 1995 / In revised form: 5 August 1995