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Redefining the deviance objective for generalised linear models

Published online by Cambridge University Press:  16 October 2012

A. C. Lovick  and
P. K. W. Lee
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Abstract

This paper defines the ‘Case Deleted’ Deviance - a new objective function for evaluating Generalised Linear Models, and applies this to a number of practical examples in the pricing of general insurance. The paper details practical approximations to enable the efficient calculation of the objective, and derives modifications to the standard Generalised Linear Modelling algorithm to allow the derivation of scaled parameters from this measure to reduce potential over fitting to historical data. These scaled parameters improve the predictiveness of the model when applied to previously unseen data points, the most likely being related to future business written. The potential for over fitting has increased due to number of factors now used, particularly in pricing personal lines business and the advent of price comparison sites which has increased the penalties of mis-estimation. New material in this paper has been included in a UK patent application No. 1020091.3.

Keywords

Generalised Linear ModellingGeneral Insurance PricingParameter UncertaintyCase DeletionDevianceNon-Linear ModellingDemand ModellingPrice Comparison Site PricingWinner's Curse.

Information

Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 17 , Issue 3 , September 2012 , pp. 491 - 509
Copyright
Copyright © Institute and Faculty of Actuaries 2012

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References

References

Anderson, D., Feldblum, S., Modlin, C., Schirmacher, D., Schirmacher, E., Thandi, N. (2007). A Practitioner's Guide to Generalized Linear Models (Third Edition), CAS Study Note.Google Scholar
Atkinson, A.C. (1987). Plots, Transformations and Regression. Oxford University Press, ISBN 978-0-198-53371-9.Google Scholar
Berry, J. (Chair), Hemming, G., Matov, G., Morris, O. (2009). Report of the Model Validation and Monitoring Personal Lines Pricing Working Party. Available at: http://www.actuaries.org.uk/research-and-resources/documents/report-model-validation-and-monitoring-personal-lines-pricing-workiGoogle Scholar
Dobson, A.J. (2001). An introduction to generalized linear models 2nd Ed. Chapman & Hall, ISBN 978-1-58488-165-8.Google Scholar
English, A. (2000–9) EMB Emblem User's Guide, EMB Software Ltd, 2000–9.Google Scholar
Hocking, R.R. (1996). Methods and applications of Linear Models. John Wiley & Sons. Inc, ISBN 978-0-471-59282-2.Google Scholar
McCullagh, P., Nelder, J.A. (1989). Generalized Linear Models 2nd Ed. Chapman & Hall, ISBN 978-0-41231-760-5.Google Scholar
Murphy, K., Lee, P., Brockman, M. (2005). Generalized Nonlinear Models: Applications to Auto. COSIS: Predictive Modelling.Google Scholar
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T. (2002). Numerical Recipes in C++: the art of scientific computing 2nd Ed. Cambridge University Press, ISBN 978-0-521-75033-4.Google Scholar

Additional reference

Smyth, G.K., Jørgensen, B. (2002). Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling. ASTIN Bulletin, Vol. 32, No. 1.Google Scholar