Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-16T21:54:18.851Z Has data issue: false hasContentIssue false
  • English
  • Français

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: b.avanzi@unsw.edu.au
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: bernard.wong@unsw.edu.au
*
E-Mail: greg.taylor@unsw.edu.au
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bateup, R. and Reed, I. (2001) Research and data analysis relevant to the development of standards and guidelines on liability valuation for general insurance. Tech. rep., Towers Perrin: The Institute of Actuaries of Australia and Tilinghast.Google Scholar
Britt, S. and Johnstone, D. (2001) The ABCs of DFA. In Institute of Actuaries of Australia (Ed.), XIIIth General Insurance Seminar.Google Scholar
Collings, S. and White, G. (2001) Apra risk margin analysis. In Institute of Actuaries of Australia (Ed.), XIIIth General Insurance Seminar.Google Scholar
De Gooijer, J.G. (2006) Detecting change-points in multidimensional stochastic processes. Computational Statistics and Data Analysis, 51, 1892–1903.CrossRefGoogle Scholar
Embrechts, P., McNeil, A.J. and Straumann, D. (2002) Correlation and Dependency in Risk Management: Properties and Pitfalls. Cambridge: Cambridge University Press.Google Scholar
England, P. and Verrall, R. (1999) Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25 (3), 281–293.Google Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. London: Chapman & Hall.Google Scholar
Kuang, D., Nielsen, B. and Nielsen, J.P. (2008a) Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika 95 (4), 987–991.CrossRefGoogle Scholar
Kuang, D., Nielsen, B. and Nielsen, J. (2008b) Identification of the age-period-cohort model and the extended chain-ladder model. Biometrika, 95 (4), 979–986.CrossRefGoogle Scholar
Kuang, D., Nielsen, B. and Nielsen, J. (2009) Chain-ladder as maximum likelihood revisited. Annals of Actuarial Science, 4 (01), 105–121.CrossRefGoogle Scholar
Lindskog, F. (2000) Linear correlation estimation. Tech. rep, RiskLab.Google Scholar
Lindskog, F. and McNeil, A.J. (2003) Common poisson shock models: Applications to insurance and credit risk modelling. Astin Bulletin, 33 (2), 209–238.CrossRefGoogle Scholar
Mack, T. and Venter, G. (2000) A comparison of stochastic models that reproduce chain ladder reserve estimates. Insurance: Mathematics and Economics, 26 (1), 101–107.Google Scholar
Meyers, G. and Shi, P. (September 2011) Loss Reserving Data Pulled From NAIC Schedule P. Available at: http://www.casact.org/research/index.cfm?fa=loss_reserves_data.Google Scholar
Mulvey, J. M., Pauling, B., Britt, S. and Morin, F. (2007) Dynamic financial analaysis for multinational insurance companies. In Handbook of Asset and Liability Management: Applications and Case Studies, 2, 543–589.CrossRefGoogle Scholar
O'Dowd, C., Smith, A. and Hardy, P. (2005) A framework for estimating uncertainty in insurance claims cost. In Institute of Actuaries of Australia (Ed.), XVth General Insurance Seminar.Google Scholar
Risk Margins Task Force (2008) A framework for assessing risk margins. In Institute of Actuaries of Australia (Ed.), XVIth General Insurance Seminar.Google Scholar
Rousseeuw, P. and Molenberghs, G. (1993) Transformation of non positive semidefinite correlation matrices. Communications in Statistics - Theory and Methods, 22 (4), 965–984.CrossRefGoogle Scholar
Shi, P. and Frees, E.W. (2011) Dependent loss reserving using copulas. ASTIN Bulletin, 41 (2), 449–486.Google Scholar
Shumway, R.H. and Stoffer, D.S. (2011) Time Series Analysis and Its Applications, 3rd Edition. Springer Texts in Statistics. New York (Dordrecht, Heidelberg, London): Springer.CrossRefGoogle Scholar
Taylor, G. (2000) Loss Reserving: An Actuarial Perspective. Huebner International Series on Risk, Insurance and Economic Security. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
Taylor, G. (2011) Maximum likelihood and estimation efficiency of the chain ladder. ASTIN Bulletin 41 (1), 131–155.Google Scholar
Taylor, G., McGuire, G. and Sullivan, J. (2008) Individual claim loss reserving conditioned by case estimates. Annals of Actuarial Science, 3 (1–2), 215–256.CrossRefGoogle Scholar
Vigen, T. (2015) Spurious correlations (last accessed on 18 march 2015 on http://www.tylervigen.com).Google Scholar
Wüthrich, M. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. New York: John Wiley & Sons.Google Scholar