Journal of East China Normal University(Natural Science) >

2019 , Vol. 2019 >Issue 1: 13 - 23

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.01.002

Mathematics

Estimation of loss reserves based on a hierarchical bayesian model

  • ZHANG Yi ,
  • LIU Zhi-qiang ,
  • ZOU Si-si ,
  • WEN Li-min
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  • 1. School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China;
    2. Department of Statistics, Jiangxi Normal University, Nanchang 330022, China

Received date: 2017-09-29

  Online published: 2019-01-24

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Abstract

Traditional loss reserve models are mainly based on aggregate loss triangles, in which the entries are obtained by summations of individual loss data. The summation procedures inevitably cause wastage of information contained in the raw individual data. Though this method is simple, it results in a larger error in the estimate of loss reserves. Individual loss reserve models emerging in recent years have failed to consider dependencies between policies. This article assumes the existence of certain common random effects between policies in the same accident year. Thus, a hierarchical bayesian model is built for individual data loss reserves. Using the ideas of credibility theory, we get the credibility estimate of loss reserves in each accident year, and thus the total reserve. In addition, the estimation of structural parameters and development factors are discussed. And the statistical properties are derived for those estimators of structural parameters. Finally, a numerical example is given to show the calculations with our estimators, and simulations are done to compare the mean square of reserve estimator between an individual loss model and an aggregate data model.

Key words： loss reserve; common effect; individual loss data; credibility estimate

Cite this article

ZHANG Yi , LIU Zhi-qiang , ZOU Si-si , WEN Li-min . Estimation of loss reserves based on a hierarchical bayesian model[J]. Journal of East China Normal University(Natural Science), 2019 , 2019(1) : 13 -23 . DOI: 10.3969/j.issn.1000-5641.2019.01.002

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