Comparing present values of life annuity of multi-life status under different dependent structure

在多生命状态各个体余寿相依的情形下,通过比较边际分布或相依结构,研究终身年金趸缴保费精算现值的差异.采用Copula函数作为相依结构的表示,分别研究:(1)假设各投保集团个体余寿之间相依结构相同的情形下,根据余寿向量在随机序意义下的大小,比较各投保集团终身年金趸缴保费精算现值的大小;(2)假设两个投保集团个体余寿有相同的分布,但个体余寿之间相依结构不相同的情形下,比较其终身年金趸缴保费精算现值的差异.     

相依情形下多生命状态年金现值的比较北大核心CSCD

在多生命状态各个体余寿相依的情形下,通过比较边际分布或相依结构,研究终身年金趸缴保费精算现值的差异.采用Copula函数作为相依结构的表示,分别研究:(1)假设各投保集团个体余寿之间相依结构相同的情形下,根据余寿向量在随机序意义下的大小,比较各投保集团终身年金趸缴保费精算现值的大小;(2)假设两个投保集团个体余寿有相同的分布,但个体余寿之间相依结构不相同的情形下,比较其终身年金趸缴保费精算现值的差异.     

随机环境影响下系统可靠性比较

本文研究随机环境影响系统相依结构的情形下,系统可靠性的随机比较,文章采用连接函数表示系统的相依结构,研究不同随机环境因子下两个系统的象限序、弱多元失效率序、n中取k系统的寿命等的随机比较,并通过实际例子进行分析.     

逆Weibull分布随机变量的随机比较

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

Ⅰ型极值分布随机变量的随机比较

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

逆Weibull分布随机变量的随机比较(英文)

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Ⅰ型极值分布随机变量的随机比较(英文)

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Archimedean copula刻画的尺度比例失效率模型的极小次序统计量的随机序北大核心CSCD

在多元链式优化序下,该文研究了两组来自于不同相依尺度比例失效率分布的最小次序统计量的随机比较.在某种数学意义下,一个由尺度比例失效率分布的不同脆弱参数和尺度参数构成的矩阵变化到另一个矩阵时,该文研究了在一定的条件下,来自于第一个尺度比例失效率分布的最小次序统计量在普通随机序下小于变化到的参数矩阵对应的尺度比例失效率分布的最小次序统计量.该文也给出了一些数值例子来说明得到的结果的正确性.     

正相依风险下离散模型的最优分红

将保险公司各期净损失相互独立的假定改进为依随机序正相依.在相依风险下,利用动态规划原理和状态空间约简,刻画了最优分红策略,证明了区域策略最优,同时讨论了值函数的性质,并给出了数值算法.其中,对涉及独立假定的结论,给出了相依条件下的相应结果,对未涉及独立假定的部分结论也做了改进.研究发现,与独立情形不同,在依随机序正相依风险下,保险公司不必以概率1破产.     

风险相依的保险投资组合研究

在个人和团体风险模型中,用s=Em=1x.表示保险投资组合的累积索赔,其中,X1,I>/1表示第i个保单产生的损失,N表示保险公司在一定时期内(例如,一年)总的索赔项数,每一个保单可能包含若干个不同的项目,假定一个保单的损失是这些不同项目索赔的总和,而一个保单的不同项目的索赔往往是相关的.Marceau et al.(1999)建立了一个相依风险模型,其中考虑了保险投资组合中个体风险之间的相依性.最近,Denuit(2001)证明了两个不同参数投资组合的索赔向量之间拉普拉斯变换序成立.本文将证明,事实上更强的随机序是成立的,并将该模型推广到团体风险模型的情形.     

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??The mean residual life (MRL) function plays a very important role in the area of reliability engineering, survival analysis, and many other fields. In this paper, we introduce and study a new stochastic order which gives stochastic comparison for mean residual life of strictly increasing concave function of two random variables. We show that this new stochastic order lies between the hazard rate and mean residual life orders. The preservation properties under mixtures are presented here. Finally, we give some applications of this new order in reliability theory.     

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??In this paper, we compare the smallest order statistics arising from multiple-outlier models when the numbers of independent and identically distributed random variables are different. Let and denote the smallest order statistics among, and, respectively, whereand. We then prove that $ and are ordered in terms of the usual stochastic order, hazard rate order and likelihood ratio order under the majorization relationship between and.     

Stochastic comparisons for time transformed exponential models

Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müller and Scarsini (2001). Here we provide conditions for the comparison, in the usual stochastic order sense and in other weaker stochastic orders, of two time transformed exponential bivariate lifetimes having different copulas. Some examples of applications are provided too.     

Optimal reinsurance with positively dependent risks

In the individual risk model, one is often concerned about positively dependent risks. Several notions of positive dependence have been proposed to describe such dependent risks. In this paper, we assume that the risks in the individual risk model are positively dependent through the stochastic ordering (PDS). The PDS risks include independent, comonotonic, conditionally stochastically increasing (CI) risks, and other interesting dependent risks. By proving the convolution preservation of the convex order for PDS random vectors, we show that in individualized reinsurance treaties, to minimize certain risk measures of the retained loss of an insurer, the excess-of-loss treaty is the optimal reinsurance form for an insurer with PDS dependent risks among a general class of individualized reinsurance contracts. This extends the study in Denuit and Vermandele (1998) on individualized reinsurance treaties to dependent risks. We also derive the explicit expressions for the retentions in the optimal excess-of-loss treaty in a two-line insurance business model.     

Comparisons on aggregate risks from two sets of heterogeneous portfolios

In this paper, we stochastically compare the aggregate risks from two heterogeneous portfolios. It is shown that under suitable conditions the more heterogeneities among aggregate risks would result in larger aggregate risks in the sense of the stochastic order. The stochastic properties of aggregate risks when the claims follow proportional hazard rates models or scale models are studied. We also provide sufficient conditions for comparing the aggregate risks arising from two sets of heterogeneous portfolios with claims having gamma distributions. In particular, the aggregate risks of portfolios from dependent samples with comonotonic dependence structures or arrangement increasing density functions are discussed. The new results established strengthen and generalize several results known in the literature including Ma (2000), Khaledi and Ahmadi (2008), Xu and Hu (2011), Xu and Balakrishnan (2011), Pan et al. (2013) and Barmalzan et al. (2015).     

关于Gamma分布的秩序统计量的随机比较

对于独立不同分布的两个Gamma样本，当它们相同的形状参数大于或等于1时，最近Korwar(2002)证明了，当它们的尺度参数满足优化序时，样本的卷积就满足似然比序．本文我们证明了，当Gamma分布的形状参数小于1时，样本的对应秩序统计量之间存在一致的一般随机序；然而当形状参数大于1时，样本对应的极大值和极小值统计量有着相反的一般随机序。     

Gompertz分布顺序统计量的一些随机比较

考虑两组相互独立的来自非齐次总体Gompertz分布的样本,给出了最小顺序统计量的反向失效率序、散度序以及凸变换序之间的比较和最大顺序统计量的普通随机序的比较.     

折现的未决赔款准备金估计的随机逼近

凸序意义下的随机界是估计具有相依性随机变量和分布的良好工具.在考虑货币时间价值的基础上,通过随机上下界的两种不同形式的凸组合对未决赔款准备金的估计进行逼近,并通过矩匹配法,给出了最优权数的计算公式.通过一个实例对所述方法进行验证.     

On stochastic comparisons of series systems with heterogeneous dependent and independent location-scale family distributed components

This paper carries out comparisons of heterogeneous series systems with location-scale family distributed components It is shown that the systems with dependent components in series sharing Archimedean copula with more dispersion in the location or scale parameters result in better performance in the sense of the usual stochastic order. Moreover, if the components are independently distributed, it is possible to obtain more generalized results as compared to the dependent set-up.