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CORRELATIONS BETWEEN INSURANCE LINES OF BUSINESS: AN ILLUSION OR A REAL PHENOMENON? SOME METHODOLOGICAL CONSIDERATIONS

Published online by Cambridge University Press:  27 January 2016

Benjamin Avanzi ,
Greg Taylor  and
Bernard Wong
Benjamin Avanzi
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia Département de Mathématiques et de Statistique, Université de Montréal, Montréal QC H3T 1J4, Canada E-Mail: [email protected]
Greg Taylor*
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia
Bernard Wong
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

This paper is concerned with dependency between business segments in the non-life insurance industry. When considering the business of an insurance company at the aggregate level, dependence structures can have a major impact in several areas of Enterprise Risk Management, such as in claims reserving and capital modelling. The accurate estimation of the diversification benefits related to the dependence structures between lines of business (LoBs) is crucial for (i) capital efficiency, as one should avoid holding unnecessarily high levels of capital, and (ii) solvency of the insurance company, as an underestimation, on the other hand, may lead to insufficient capitalisation and safety. There seems to be a great deal of preconception as to how dependent insurance claims should be. Often, presence of dependence is taken as a given and rarely discussed or challenged, perhaps because of the lack of extensive datasets to be publicly analysed. In this paper, we take a different approach, and consider how much correlation some real datasets actually display (the Meyers–Shi dataset from the USA, and the AUSI dataset from Australia). We develop a simple theoretical framework that enables us to explain how and why correlations can be illusory (and what we mean by that). We show with some real examples that, sometimes, most (if not all) of the correlation can be “explained” by an appropriate methodology. Two major conclusions stem from our analysis.

  1. 1. In any attempt to measure cross-LoB correlations, careful modelling of the data needs to be the order of the day. The exercise will not be well served by rough modelling, such as the use of simple chain ladders, and may indeed result in the prescription of excessive risk margins and/or capital margins.

  2. 2. Such empirical evidence as examined in the paper reveals cross-LoB correlations that vary only in the range zero to very modest. There is little evidence in favour of the high correlation assumed in some jurisdictions. The evidence suggests that these assumptions derived from either poor modelling or a misconception of the cross-LoB dependencies relevant to the purpose to which they are applied.

Keywords

Actuarial modelsdependencecapital margincorrelationreal datareservingrisk margin
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 2 , May 2016 , pp. 225 - 263
Copyright
Copyright © Astin Bulletin 2016 

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