带有免赔额调整的车险奖惩系统及其最优自留额

考虑了带有免赔额调整的车险奖惩系统.利用无差别原理,将奖惩系统惩罚等级中增收保费的部分或全部用添加免赔额的方式替代,给出了替代后奖惩系统最优自留额的递推计算公式.最后,给出一个例子并分析了免赔额与平均最优自留额的关系.     

奖惩系统在随机优序下的极小与极大平稳分布

奖惩系统(Bonus-M a lus System)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.文[1]在最一般的框架下,给出了奖惩系统的数学建模与稳态分析.本文将进一步证明,文[1]中给出的奖惩系统两种特定的平稳分布恰分别是奖惩系统在随机优序下的极小与极大平稳分布.特别地,基于这一事实严格证明了文[1]提出的有关封闭型奖惩系统年度总保费的一个猜想.     

考虑个体保单风险特征的最优奖惩系统

奖惩系统在汽车保险中的应用非常普遍。论文首先介绍和讨论了泊松-伽马假设下的最优奖惩系统及其性质;其次在假设个体保单的索赔频率服从二项分布,而二项分布的一个参数服从贝塔分布的条件下,建立了一种考虑个体保单风险特征信息的最优奖惩系统,其中风险特征信息可以通过广义线性模型的形式引入奖惩系统;然后在假设个体保单的索赔频率服从负二项分布,而负二项分布的一个参数服从贝塔分布的条件下,建立了另一个最优奖惩系统;最后讨论了这两个奖惩系统的性质和应用。     

生态文明发展状况的动态奖惩评价及应用

推进生态文明建设是全面建设小康社会的新要求。本文提出一种具有奖惩特征及引导作用的生态文明评价模型。首先,根据被评价对象的实际发展趋势以及不同被评价对象同一时刻评价值的平均增量确定各被评价对象不同时刻评价值的理想点;其次,根据被评价对象实际评价值与理想点之间的差值确定被评价对象的奖惩情况、奖惩因子以及具有奖惩特征的动态综合评价值;最后,应用该方法对中国10个省域的生态文明状况进行了评价与比较分析。     

基于索赔额与应负责任的奖惩系统

在机动车保险中，仅仅基于索赔次数的奖惩系统对那些有着小索赔的保单持有人不公平。在本文，我们考虑索赔额的大小及责任归属，建立一个基于索赔额与应负责任的奖惩系统。     

稳健贝叶斯方法下考虑理赔次数因素的汽车保险奖惩系统

本文将稳健贝叶斯方法用于构造汽车保险奖惩系统并分析其敏感性. 用先验分布集合$\Gamma_\varepsilon=\{\pi$:$\pi=(1-\varepsilon)\pi_0+\varepsilon q,q\inQ\}$描述保单组合的风险异质性. 从而得到混合先验分布下的奖惩系统; 当$q$ 在$Q$内变化时, 对奖惩系统进行敏感性分析.     

流态化非均匀结构的概率模型

通过对实验数据的直方图的分析和统计检验的手段,找到了定量描述一类气固流化订系统非均匀结构动态行淡的概率分布－七参娄威布尔分布,提示了这种复杂系统内非均匀性的一些规律,模拟结果是理想的。     

具有位相型随机补货提前期的PH退化可修系统及其最优更换策略

将几何过程与PH分布相结合, 讨论一个带有位相型随机补货提前期的PH退化可修系统.通过建立最小生成元$Q$矩阵,获得了系统在稳态情形下的状态概率分布向量及其数值解.根据上述研究结果同时也得到了系统的几个重要可靠性指标. 进一步地,还考虑了基于部件故障次数的订购策略和更换策略,导出系统单位时间平均运行成本的解析表达式并给出一个确定最优$N$策略的数值算例.     

带有止步和N-策略的M/H2/1多重休假排队系统

本文研究一个带有止步和N-策略的M/H2/1多重休假排队系统。利用拟生灭过程与矩阵几何解的方法求出了系统的稳态平衡条件和稳态概率分布。此外,本文还求出了系统的一些性能指标。     

M/M/c休假排队系统稳态分布的数值计算

从数值计算角度研究M/M/c休假排队系统稳定状态的概率分布.采用GMRES方法求解概率分布向量所满足的大型线性方程,构造了一个循环预处理算子加速GMRES方法的收敛.数值实例验证了该算法的优越性.     

Bayesian inspection model with the negative binomial prior in the presence of inspection errors

One of the basic assumptions in Bayesian inspection models is that we have some prior knowledge about the number of defects in a certain product or software system. The prior knowledge can be often described as a probability distribution (e.g., Poisson distribution). In the paper, we propose three conditions that should be put forth as desirable properties for a prior probability distribution of the number of defects in the product. We review various prior probability distributions and test if they meet those conditions. The negative binomial distribution is found to be the only one that satisfies all the desirable conditions. With the negative binomial prior, we analyze the effects of various parameters on the Bayesian estimate of the number of undetected errors still remaining in the product.     

再论机动车辆保险的精算模型及其应用

通过对非参数混合泊松模型的分析 ,我们发现用此类模型建立无赔款优待系统是不合适的 .在文中我们使用 Hofmann分布为我国一家保险公司的索赠数据进行拟合 ,效果令人满意 ,然后导出最优无赔款优待系统和零效用原理下的无赔款优待系统     

Comments on “Statistical reasoning with set-valued information: Ontic vs. epistemic view” by Inés Couso and Didier Dubois

I discuss some aspects of the distinction between ontic and epistemic views of sets as representation of imprecise or incomplete information. In particular, I consider its implications on imprecise probability representations: credal sets and sets of desirable gambles. It is emphasized that the interpretation of the same mathematical object can be different depending on the point of view from which this element is considered. In the case of a fuzzy information on a random variable, it is possible to define a possibility distribution on the simplex of probability distributions. I add some comments about the properties of this possibility distribution.     

Sets of desirable gambles: Conditioning, representation, and precise probabilities

The theory of sets of desirable gambles is a very general model which covers most of the existing theories for imprecise probability as special cases; it has a clear and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, much work remains to be done until the theory of desirable gambles can be considered as generally applicable to reasoning tasks as other approaches to imprecise probability are. This paper gives an overview of some of the fundamental concepts for reasoning with uncertainty expressed in terms of desirable gambles in the finite case, provides a characterization of regular extension, and studies the nature of maximally coherent sets of desirable gambles, which correspond to finite sequences of probability distributions, each one of them defined on the set where the previous one assigns probability zero.     

Stochastic Breakeven Points

When the probability of a negative unit contribution is non-negligible, desirable and undesirable data configurations may map into the same breakeven point. In the general case, the decision relevance of a breakeven point probability distribution is rather obscure. Assuming bivariate normality, with a "small" probability of a negative denominator, then an approximation procedure based on the Geary-Hinkley transformation is a convenient and powerful means of obtaining information about the breakeven point probability distribution. Hence, for practical purposes it may be unnecessary to resort to computer simulation or to numerical integration of the complex exact density function of the breakeven point.     

A COMPARISON BETWEEN TWO KINDS OF BMS BASED ON DIFFERENT CREDIBILITY

The paper develops a design of optimal Bonus-Malus System （BMS） based on exact equitable credibility,in which the relative error function is taken as loss function. In BMS,both the frequency and the severity components are considered. This design is compared with traditional BMS derived from classical squared-error loss function.     

GPSJ分布类下的无赔款优待系统及应用

本文利用GPSJ1的性质,导出此分布类下的最优无赔款优待系统和零效用原理下的无赔款优待系统。同时以我国一家保险公司的索赔数据为例,对本文给出的结果进行说明。     

Gradient modeling for multivariate quantitative data

We propose a new parametric model for continuous data, a “g-model”, on the basis of gradient maps of convex functions. It is known that any multivariate probability density on the Euclidean space is uniquely transformed to any other density by using the gradient map of a convex function. Therefore the statistical modeling for quantitative data is equivalent to design of the gradient maps. The explicit expression for the gradient map enables us the exact sampling from the corresponding probability distribution. We define the g-model as a convex subset of the space of all gradient maps. It is shown that the g-model has many desirable properties such as the concavity of the log-likelihood function. An application to detect the three-dimensional interaction of data is investigated.