基于广义线性模型的个体索赔RBNS准备金评估

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基于广义线性模型的个体索赔RBNS准备金评估张林娜¹, 温利民¹, 王江峰², 王伟³1. 江西师范大学数学与信息科学学院, 南昌 330022;
2. 浙江工商大学统计系, 杭州 310018;
3. 宁波大学数学系, 宁波 315211 Evaluation of Individual RBNS Loss Reserving Based on Generalized Linear Model ZHANG Linna¹, WEN Limin¹, WANG Jiangfeng², WANG Wei³1. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
2. Department of Statistics, Zhejiang Gongshang University, Hongzhou 310018, China;
3. Department of Mathematics, Ning Bo University, Ningbo 315211, China

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摘要基于个体索赔模型对准备金的评估已成为准备金评估研究的重要内容.本文基于广义线性模型，对个体索赔额及索赔数目建立责任准备金模型，给出未决赔款责任准备金的期望及方差.进而，根据样本数据对未知参数求解极大似然估计，并讨论了估计的强相合性和渐近正态性.并得到责任准备金的估计及其预测均方误差.最后，通过数值模拟的方法将本文得到的估计与链梯法进行比较，结果显示我们的估计明显优于链梯法估计.

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收稿日期: 2015-06-04

PACS:

O212

基金资助:国家自然科学基金（71361015），江西省自然科学基金重点项目（20171ACB21022），江西省社科十二五规划项目（15WDZT10）以及教育部人文社科基金（（15YJC910010，14YJC630085）资助.

引用本文:

张林娜, 温利民, 王江峰, 王伟. 基于广义线性模型的个体索赔RBNS准备金评估[J]. 应用数学学报, 2017, 40(4): 573-593. ZHANG Linna, WEN Limin, WANG Jiangfeng, WANG Wei. Evaluation of Individual RBNS Loss Reserving Based on Generalized Linear Model. Acta Mathematicae Applicatae Sinica, 2017, 40(4): 573-593.

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