相依风险模型下风险保费的信度估计

建立了风险之间呈现某种特殊相依结构的信度模型.利用正交投影的方法,得到了相依风险模型下的Bühlmann信度保费和Bühlmann-Straub信度保费,并讨论了信度估计的统计性质.结论表明,在风险之间呈现相依结构时,信度预测是个体索赔均值,总索赔均值和聚合保费三者的加权和,从而推广了经典的信度理论.     

失真风险保费的最优经验厘定

研究了贝叶斯模型中失真风险保费的经验厘定问题.通过引入分布函数的加权积分损失函数,利用信度理论的方法最小化期望损失得到分布函数的最优线性估计,进而得到失真风险保费的两个信度估计,并对信度估计的统计性质进行了比较.文章还讨论了失真函数和权重函数的选取问题,给出了结构参数的估计方法,证明了估计的无偏性和相合性.最后,利用数值模拟的方法验证了估计的收敛情况,并对不同失真函数下的收敛情况进行了比较.     

具有风险相依结构的平衡信度估计

在保险实务中,风险之间具有一定的相依结构.通过考虑保费的目标估计来对风险保费进行了研究,采用正交投影的方法求解了最优问题,在平衡损失函数下得到了风险等相关的齐次和非齐次信度估计.结果表明得到的信度估计具有经典信度模型的加权形式.     

新型广义加权保费原理下风险保费的信度估计

本文研究了新型广义加权保费原理下风险保费的信度估计问题.利用了损失函数法,将新型广义加权保费原理定义为新型广义加权损失函数下风险的最优估计.在该损失函数下,把估计限定在经验估计的线性组合,根据均方误差最小原则得到风险保费的信度估计,并证明了信度估计的相合性,最后,在Esscher保费原理下对信度估计的相合性进行模拟验证,并在指数保费原理下与前人的结果进行了比较,结果发现已有的研究只是本文的一种特殊情况.     

熵损失函数下的信度模型

本文研究了信度模型问题.利用熵损失函数,获得了风险保费的信度估计和经验Bayes信度估计.所获结果是对现有风险保费信度估计和经验Bayes信度估计的一个补充.     

矩相关保费原理中风险保费的经验厘定

在传统的B¨uhlmann信度理论中,信度估计仅仅适合净保费原理,并且很难直接推广到更一般的保费原理中.本文根据随机变量的矩母函数定义一种统一的保费原理—矩相关保费原理,进而,将信度理论的思想运用于估计风险随机变量的矩母函数,给出矩相关保费原理中风险保费的经验厘定估计,并证明估计的统计性质.结果表明,在净保费原理和指数保费原理中,已有的信度估计是本文估计的特殊情形;在方差保费原理中,本文得到的估计要优于已有的信度估计.最后,通过数值模拟的方法验证新的信度估计的相合性和渐近正态性,并在小样本条件下比较本文估计与已有估计的均方误差.     

平衡指数损失函数下具有通货膨胀因子的信度估计

在经典的信度保费模型中,得到的信度保费估计均是考虑的是纯保费,然而在保险实务中,保险公司收取的保费不可能是纯保费,必须具有正的安全负荷.在平衡指数损失函数下给出了具有通货膨胀因子的信度估计.结果表明,在考虑历史索赔数据的样本函数的情况下,当选取一个合适的权重,便可以得到下一期的最优信度保费估计.结论推广了仅在平方损失函数下得到的信度保费.     

具有风险相依结构的Bhlmann信度模型

在经典的Bühlmann信度模型中,一般假设风险之间是相互独立的.但在实际应用中,这种假设与实际不吻合.本文建立了风险相依情况下的Bühlmann信度模型,并得到了相应的非齐次与齐次信度估计.最后,对该结论与经典Bühlmann信度估计做了比较,得出较好的结论.     

基于核估计下概率密度函数的信度模型

结合核估计和信度理论的思想,建立了密度函数的Bayes模型,将条件密度函数的估计限定在核函数的线性组合中,通过最小化期望积分平方损失函数,得到了密度函数的信度估计,并研究了估计的统计性质,讨论了窗宽的最优选择方法;进而基于密度函数的信度估计,得到了各种保费原理中风险保费的信度估计,并与传统的信度估计进行了比较.     

平衡指数损失函数下的信度保费

在经典的信度保费模型中,得到的信度保费估计均是考虑的是纯保费,然而在保险实务中,保险公司收取的保费不可能是纯保费,必须具有正的安全负荷.在平衡指数损失函数下,研究了多合同的信度保费模型.利用正交投影方法,得到了未来保费的信度估计.最后对估计进行了数值模拟.     

A generalization of the credibility theory obtained by using the weighted balanced loss function

In this paper an alternative to the usual credibility premium that arises for weighted balanced loss function is considered. This is a generalized loss function which includes as a particular case the weighted quadratic loss function traditionally used in actuarial science. From this function credibility premiums under appropriate likelihood and priors can be derived. By using weighted balanced loss function we obtain, first, generalized credibility premiums that contain as particular cases other credibility premiums in the literature and second, a generalization of the well-known distribution free approach in [Bühlmann, H., 1967. Experience rating and credibility. Astin Bull. 4 (3), 199-207].     

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??In classical credibility theory, the claim amounts of different
insurance policies in a portfolio are assumed to be independent and the premiums are derived
under squared-error loss function. Wen et al. (2012) studied the credibility models with a
dependence structure among the claim amounts of one insurance policy that is called time
changeable effects and obtained the credibility formula. In this paper, we generalized this
dependence structure called time changeable effects to the claim amounts of different
insurance policies in a portfolio. Credibility premiums are obtained for Buhlmann and
Buhlmann-Straub credibility models with dependence structure under balanced loss function.     

平衡损失函数下的信度模型

保险公司对保费进行定价时,一般是有一个目标保费. 本文结合信度定价原理, 考虑保费的目标估计,得到平衡损失函数下的信度估计. 并对其未知参数进行估计,得到相应的经验Bayes信度估计.     

The credibility premiums for models with dependence induced by common effects

In classical Bühlmann credibility models, claims are assumed to be independent between different risks. In many practical situations, however, this assumption may be violated because there are situations that could drive possible relationship among the insured individuals. This paper aims to extend the Bühlmann and Bühlmann-Straub credibility models to account for a special type of dependence between risks induced by common stochastic effects. By means of the projection method, the corresponding credibility premiums are obtained, which generalize some well known existing results in credibility theory.     

具有共同效应的信度回归模型

在经典的Hachemeister(1975)信度回归模型中,各个风险被假定为相互独立的.本文假设风险之间存在由共同效应导致的风险相依,建立了共同效应的信度回归模型,得到未来索赔的信度预测与风险参数的信度估计.结论表明,在共同效应模型,信度估计仍然是个体索赔数据与聚合保费的加权和.     

Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation

The purpose of this paper is to explore and compare the credibility premiums in generalized zero-inflated count models for panel data. Predictive premiums based on quadratic loss and exponential loss are derived. It is shown that the credibility premiums of the zero-inflated model allow for more flexibility in the prediction. Indeed, the future premiums not only depend on the number of past claims, but also on the number of insured periods with at least one claim. The model also offers another way of analysing the hunger for bonus phenomenon. The accident distribution is obtained from the zero-inflated distribution used to model the claims distribution, which can in turn be used to evaluate the impact of various credibility premiums on the reported accident distribution. This way of analysing the claims data gives another point of view on the research conducted on the development of statistical models for predicting accidents. A numerical illustration supports this discussion.     

The credibility premiums for exponential principle

In the classical credibility theory, the credibility premium is derived on the basis of pure premium. However, the insurance practice demands that the premium must be charged under some adaptable premium principle and serves the purpose for insurance business. In this paper, the balanced credibility models have been built under exponential principle, and the credibility estimator of individual exponential premium is derived. This result is also extended to the versions of multitude contracts, and the estimation of the structure parameters is investigated. Finally, the simulations have been introduced to show the consistency of the credibility estimator and its differences from the classical one.     

Tolerance intervals in risk theory

Up to now, the main aim of credibility theory has been to provide statistical models which allow for estimating (net) risk premiums appropriately. In the present note, a simple credibility model based on the percentile principle is introduced. It turns out that there are close connections between the resulting credibility premiums and statistical tolerance limits.