Claim dependence induced by common effects in hierarchical credibility models

Mahdi Ebrahimzadeh, Noor Akma Ibrahim, Abdul Aziz Jemain, Adem Kilicman

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In the usual credibility model, observations are made of a risk or group of risks selected from a population, and claims are assumed to be independent among different risks. However, there are some problems in practical applications and this assumption may be violated in some situations. Some credibility models allow for one source of claim dependence only, that is, across time for an individual insured risk or a group of homogeneous insured risks. Some other credibility models have been developed on a two-level common effects model that allows for two possible sources of dependence, namely, across time for the same individual risk and between risks. In this paper, we argue for the notion of modeling claim dependence on a three-level common effects model that allows for three possible sources of dependence, namely, across portfolios, across individuals and simultaneously across time within individuals. We also obtain the corresponding credibility premiums hierarchically using the projection method. Then we derive the general hierarchical structure or multi-level credibility premiums for the models with h-level of common effects.

Original languageEnglish
Pages (from-to)2673-2700
Number of pages28
JournalCommunications in Statistics - Theory and Methods
Volume42
Issue number18
DOIs
Publication statusPublished - 17 Sep 2013

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Credibility
Model
Hierarchical Structure
Projection Method
Modeling

Keywords

  • Claim dependence
  • Common effects
  • Credibility models
  • Hierarchical structure

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Claim dependence induced by common effects in hierarchical credibility models. / Ebrahimzadeh, Mahdi; Ibrahim, Noor Akma; Jemain, Abdul Aziz; Kilicman, Adem.

In: Communications in Statistics - Theory and Methods, Vol. 42, No. 18, 17.09.2013, p. 2673-2700.

Research output: Contribution to journalArticle

Ebrahimzadeh, Mahdi ; Ibrahim, Noor Akma ; Jemain, Abdul Aziz ; Kilicman, Adem. / Claim dependence induced by common effects in hierarchical credibility models. In: Communications in Statistics - Theory and Methods. 2013 ; Vol. 42, No. 18. pp. 2673-2700.
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