具有两水平共同效应的平衡分位数信度模型
The Balanced Quantile Credibility Model with Two-Level Common Effects
DOI: 10.12677/AAM.2023.126292, PDF,    科研立项经费支持
作者: 殷 铭, 张 强*：宁夏大学数学统计学院，宁夏 银川
关键词: 平衡损失函数；分位数信度；共同效应；正交投影；Balanced Loss Function； Quantile Credibility； Common Effects； Orthogonal Projection
摘要: 经典的信度模型主要是基于风险间相互独立这一假设在均方损失函数下建立的，然而，这一假设与实际并不相符。事实上，风险间通常存在着某种相依性。本文将分位数与信度模型相结合，并分别考虑组合风险间和个体风险间的相依性，在平衡损失函数下构建具有两水平共同效应的分位数信度模型。利用正交投影方法，得到了平衡损失函数下p分位数风险保费的非齐次和齐次信度估计。结果表明p分位数风险保费的信度估计具有类似经典信度模型的加权形式，推广了的已有的研究结果。
Abstract: The classical credibility model is mainly built based on the assumption that risks are independent from each other under the mean square loss function. However, this assumption is not consistent with the reality. In fact, there is usually some correlation between risks. In this paper, quantile and credibility models are combined, and dependence across individual risks and over portfolio risks is considered respectively. Then, the p quantile credibility model with two common effects is built under the balance loss function. By applying the method of orthogonal projection, the correspond-ing non-homogeneous and homogeneous credibility estimators for the p quantile risk premium are obtained. The results show that the credibility estimators have the classical model weighted form, thus extends the existing results.
文章引用：殷铭, 张强. 具有两水平共同效应的平衡分位数信度模型[J]. 应用数学进展, 2023, 12(6): 2904-2914. https://doi.org/10.12677/AAM.2023.126292

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