Journal
INSURANCE MATHEMATICS & ECONOMICS
Volume 70, Issue -, Pages 205-215Publisher
ELSEVIER
DOI: 10.1016/j.insmatheco.2016.06.006
Keywords
Aggregate claims model; Claim frequency; Claim severity; Dependence; Exponential dispersion models; Generalized linear model; Loss cost
Categories
Funding
- Canada Research Chairs Program
- Natural Sciences and Engineering Research Council of Canada [RGPIN/39476-2011, RGPIN/36860-2012]
- Canadian Statistical Sciences Institute
- Fonds de recherche du Quebec-Nature et technologies [2015-PR-183236]
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Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this often unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. In addition to being easy to implement, this modeling strategy has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium is the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpreted correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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