共查询到18条相似文献,搜索用时 125 毫秒
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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. 相似文献
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《数学的实践与认识》2015,(19)
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
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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
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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. 相似文献
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Usual credibility estimators are linear functions of the observable random variables. Semilinear credibility estimators are linear functions of some function ? of the observable random variables. The estimators mainly considered in this paper are linear functions of several functions ?1,?,?r of the observable random variables. 相似文献
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《Insurance: Mathematics and Economics》1988,7(2):113-122
In the present paper we study credibility estimators with geometric weights in the framework of experience rating in motor insurance. We discuss how to find optimal weights. The estimators are compared with the traditional credibility estimators and shown to be more robust against a certain type of violations against the model assumptions. We also discuss advantages and disadvantages relative to ordinary bonus—malus systems. 相似文献
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Erhard Kremer 《Bl?tter der DGVFM》1990,19(4):313-317
Since some time so-called credibility estimators with geometric weights are of some practical importance. As alternatives one can use so-called exponential smoothing credibility estimators. In the present paper the second ones are prepared for practical application. 相似文献
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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
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Second order (s.o.) Bayes estimators, being the main tool in the s.o. optimal statistical theory, provides a natural basis for a new approach to credibility evaluation. For the cases, where the classical credibility formula fails in the sense that it does no longer represent the predicted mean, this approach suggests an s.o. modified credibility formula, which approximately (in some sense) equals the predicted mean even for small size samples. The results are applied to the important class of location dispersion distributions and are illustrated by a number of numerical experiments. 相似文献
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Blätter der DGVFM - In a dynamic linear model the credibility estimator is given by the famous Kalman-filter algorithm. By inserting adequate parameter estimators one gets an empirical... 相似文献