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1.
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.  相似文献   

2.
王娜娜 《数学杂志》2015,35(6):1372-1378
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.  相似文献   

3.
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.  相似文献   

4.
在经典的信度理论中,一个保单组合的各风险之间是相互独立的,同时从二次损失函数中推导出信度保费.(Wen et al.,2009)给出了风险间具有共同效应的特殊的相关结构的信度保费表达式.本文在平衡损失函数下考虑此种风险结构的信度理论,特别地得到了Bühlmann和Bühlmann-Straub模型的信度保费表达式.  相似文献   

5.
程兵  陈萍 《经济数学》2016,(1):80-83
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.  相似文献   

6.
在非寿险分类费率厘定中,广义线性模型的应用十分普遍,但当某些费率因子的水平数很多时(本文称之为多水平因子),广义线性模型的估计结果将不可靠。解决此类问题的一种方法是把多水平费率因子作为随机效应处理。将多水平费率因子作为随机效应处理可以采取下述三种方法:(1)分别用广义线性模型和信度模型估计普通费率因子和多水平因子,通过广义线性模型与Buhlmann-Straub信度模型的迭代应用预测索赔频率和索赔强度;(2)应用广义线性混合模型分别预测索赔频率和索赔强度;(3)直接对经验纯保费数据建立Tweedie混合效应模型。本文把上述模型应用于中国车损险实际数据的研究结果表明,这三种方法比较接近,但从总体上看,广义线性混合模型的估计结果更加可取。  相似文献   

7.
具有线性趋势的回归信度模型中的估计和检验   总被引:1,自引:0,他引:1       下载免费PDF全文
研究具有线性趋势回归信度模型的参数估计和检验. 对该模型的回归系数和随机效应的方差,利用正交变换法得到了它们的极大似然估计, 并得到了参数的无偏估计. 对随机效应和是否有线性趋势采用似然比检验, 得到了似然统计量较好的近似$P$值, 并对检验的功效进行了模拟研究.  相似文献   

8.
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.  相似文献   

9.
本文建立了贝叶斯模型,讨论了帕累托索赔额分布中参数的估计问题,得到了风险参数的极大似然估计、贝叶斯估计和信度估计,并证明了这些估计的强相合性.在均方误差的意义下比较了这些估计的好坏,并通过数值模拟对均方误差进行了验证,结果表明,贝叶斯估计比其他估计具有较小的均方误差.最后,给出了结构参数的估计并证明了经验贝叶斯估计和经验贝叶斯信度估计的渐近最优性.  相似文献   

10.
在经典的信度理论中,信度保费是在净保费原理下得到的. 但是, 保险商业中, 保险公司要求制定的保费必须适用于某合适的保费原理以适应具体的保险商业的需要. 本文建立了指数保费原理下的完全经验厘定模型, 得到了风险保费的信度估计和经验Bayes 信度估计, 并讨论了结构参数的估计及其性质. 最后证明了多合同模型的经验Bayes 信度估计的渐近最优性  相似文献   

11.
In insurance (or in finance) practice, in a regression setting, there are cases where the error distribution is not normal and other cases where the set of data is contaminated due to outlier events. In such cases the classical credibility regression models lead to an unsatisfactory behavior of credibility estimators, and it is more appropriate to use quantile regression instead of the ordinary least squares estimation. However, these quantile credibility models cannot perform effectively when the set of data has nested (hierarchical) structure. This paper develops credibility models for regression quantiles with nested classification as an alternative to Norberg’s (1986) approach of random coefficient regression model with multi-stage nested classification. This paper illustrates two types of applications, one with insurance data and one with Fama/French financial data.  相似文献   

12.
平衡损失函数下的信度模型   总被引:2,自引:0,他引:2       下载免费PDF全文
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.  相似文献   

13.
In actuarial practice, regression models serve as a popular statistical tool for analyzing insurance data and tariff ratemaking. In this paper, we consider classical credibility models that can be embedded within the framework of mixed linear models. For inference about fixed effects and variance components, likelihood-based methods such as (restricted) maximum likelihood estimators are commonly pursued. However, it is well-known that these standard and fully efficient estimators are extremely sensitive to small deviations from hypothesized normality of random components as well as to the occurrence of outliers. To obtain better estimators for premium calculation and prediction of future claims, various robust methods have been successfully adapted to credibility theory in the actuarial literature. The objective of this work is to develop robust and efficient methods for credibility when heavy-tailed claims are approximately log-location-scale distributed. To accomplish that, we first show how to express additive credibility models such as Bühlmann-Straub and Hachemeister ones as mixed linear models with symmetric or asymmetric errors. Then, we adjust adaptively truncated likelihood methods and compute highly robust credibility estimates for the ordinary but heavy-tailed claims part. Finally, we treat the identified excess claims separately and find robust-efficient credibility premiums. Practical performance of this approach is examined-via simulations-under several contaminating scenarios. A widely studied real-data set from workers’ compensation insurance is used to illustrate functional capabilities of the new robust credibility estimators.  相似文献   

14.
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.  相似文献   

15.
In this paper, we define two restricted estimators for the regression parameters in a multiple linear regression model with measurement errors when prior information for the parameters is available. We then construct two sets of improved estimators which include the preliminary test estimator, the Stein-type estimator and the positive rule Stein type estimator for both slope and intercept, and examine their statistical properties such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks. We remove the distribution assumption on the error term, which was generally imposed in the literature, but provide a more general investigation of comparison of the quadratic risks for these estimators. Simulation studies illustrate the finite-sample performance of the proposed estimators, which are then used to analyze a dataset from the Nurses Health Study.  相似文献   

16.
The problem of simultaneous estimation of the regression parameters in a multiple regression model with measurement errors is considered when it is suspected that the regression parameter vector may be the null-vector with some degree of uncertainty. In this regard, we propose two sets of four estimators, namely, (i) the unrestricted estimator, (ii) the preliminary test estimator, (iii) the Stein-type estimator and (iv) the postive-rule Stein-type estimator. In an asymptotic setup, properties of these estimators are studied based on asymptotic distributional bias, MSE matrices, and risks under a quadratic loss function. In addition to the asymptotic dominance of the Stein-type estimators, the paper contains discussion of dominating confidence sets based on the Stein-type estimation. Asymptotic analysis is considered based on a sequence of local alternatives to obtain the desired results.  相似文献   

17.
Semiparametric mixture regression models have recently been proposed to model competing risks data in survival analysis. In particular, Ng and McLachlan (Stat Med 22:1097–1111, 2003) and Escarela and Bowater (Commun Stat Theory Methods 37:277–293, 2008) have investigated the computational issues associated with the nonparametric maximum likelihood estimation method in a multinomial logistic/proportional hazards mixture model. In this work, we rigorously establish the existence, consistency, and asymptotic normality of the resulting nonparametric maximum likelihood estimators. We also propose consistent variance estimators for both the finite and infinite dimensional parameters in this model.  相似文献   

18.
In the linear regression model with ellipsoidal parameter constraints, the problem of estimating the unknown parameter vector is studied. A well-described subclass of Bayes linear estimators is proposed in the paper. It is shown that for each member of this subclass, a generalized quadratic risk function exists so that the estimator is minimax. Moreover, some of the proposed Bayes linear estimators are admissible with respect to all possible generalized quadratic risks. Also, a necessary and sufficient condition is given to ensure that the considered Bayes linear estimator improves the least squares estimator over the whole ellipsoid whatever generalized risk function is chosen.  相似文献   

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