The credibility premiums under generalized weighted loss functions
The credibility premiums under generalized weighted loss functions
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DOI：
10.3934/jimo.2009.5.893
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发表时间：
2009-08
影响因子：
1.3
通讯作者：
Limin Wen;Xianyi Wu;X. Zhao
中科院分区：
文献类型：
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作者：
Limin Wen;Xianyi Wu;X. Zhao
在经典的信用理论中，几乎所有的信用溢价模型都是建立在纯溢价的基础上的。然而，保险实践要求保费必须具有正的安全负荷。本文考虑由广义损失函数诱导的溢价原理，该广义损失函数可以为溢价原理提供正安全载荷。在这种广义损失函数下，我们推导出了它的贝叶斯溢价和两种类型的可信度溢价。两种可信度溢价都是集体溢价与历史索赔的某些函数的近似凸组合；在第一种情况下，该函数在历史索赔中是线性的，相应的可信度溢价是不一致的，而在另一种情况下，该函数被视为个人溢价的经验版本，相应的可信度溢价收敛于个人溢价。
In the classical credibility theory, almost all the credibility premium models are built on the basis of pure premium. However, the insurance practice demands that the premium must have a positive safety loading. In this paper, we consider the premium principle induced by a generalized loss function that can provide the premium principle with\ a positive safety loading. Under this generalized loss function, we derive its Bayes premium and two types of credibility premiums. Both credibility premiums are approximately convex combinations of the collective premium and some functions of the historical claims; while in a first case the function is linear in the historical claims and the corresponding credibility premium is not consistency, in the other one the function is taken as an empirical version of the individual premium and the corresponding credibility premium converges to the individual premium.