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MODELING THE NUMBER OF INSURED HOUSEHOLDS IN AN INSURANCE PORTFOLIO USING QUEUING THEORY

Published online by Cambridge University Press:  28 March 2016

Jean-Philippe Boucher  and
Guillaume Couture-Piché
Jean-Philippe Boucher*
Affiliation:
Quantact/Département de mathématiques, UQAM, Montréal, Québec, Canada
Guillaume Couture-Piché
Affiliation:
Quantact/Département de mathématiques, UQAM, Montréal, Québec, Canada E-Mail: couture-piche.guillaume@courrier.uqam.ca
*
E-Mail: boucher.jean-philippe@uqam.ca
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Abstract

In this paper, we use queuing theory to model the number of insured households in an insurance portfolio. The model is based on an idea from Boucher and Couture-Piché (2015), who use a queuing theory model to estimate the number of insured cars on an insurance contract. Similarly, the proposed model includes households already insured, but the modeling approach is modified to include new households that could be added to the portfolio. For each household, we also use the queuing theory model to estimate the number of insured cars. We analyze an insurance portfolio from a Canadian insurance company to support this discussion. Statistical inference techniques serve to estimate each parameter of the model, even in cases where some explanatory variables are included in each of these parameters. We show that the proposed model offers a reasonable approximation of what is observed, but we also highlight the situations where the model should be improved. By assuming that the insurance company makes a $1 profit for each one-year car exposure, the proposed approach allows us to determine a global value of the insurance portfolio of an insurer based on the customer equity concept.

Keywords

Queuing theorycustomer equitypoisson processcount distributionStatistical inference
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 2 , May 2016 , pp. 401 - 430
Copyright
Copyright © Astin Bulletin 2016 

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References

Benes, V. E. (1957a). Fluctuations of telephone traffic. Bell System Technical Journal, 36, 965–973.CrossRefGoogle Scholar
Boucher, J.-P. and Couture-Piché, G. (2015) Modeling the number of Insureds' cars using queuing theory. Insurance: Mathematics and Economics, 64, 67–76.Google Scholar
Eick, S.G., Massey, W.A. and Whitt, W. (1993) Mt/G/∞ queues with sinusoidal arrival rates. Management Science, 39 (2), 241–252.Google Scholar
Gross, D., Shortle, J.F., Thompson, J.M. and Harris, C.M. (2008) Fundamentals of Queuing Theory (Wiley Series in Probability and Statistics), 4th ed.New York, NY: Wiley-Interscience.Google Scholar
Guillén, M., Nielsen, J.P., Scheike, T.H. and Pérez-Marín, A.M. (2012) Time-varying effects in the analysis of customer loyalty: A case study in insurance. Expert Systems with Applications, 39 (3), 3551–3558.CrossRefGoogle Scholar
Guelman, L., Guillén, M. and Pérez-Marín, A.M. (2014) A survey of personalized treatment models for pricing strategies in insurance. Insurance: Mathematics and Economics, 58 (1), 68–76.Google Scholar
Guelman, L., Guillén, M. and Pérez-Marín, A.M. (2015) “Uplift Random Forests” Cybernetics & Systems, Special issue on Intelligent Systems in Business and Economics, 46 (3–4). 230–248.Google Scholar
Newell, G. (1982) Applications of Queuing Theory, Monographs on Statistics and Applied Probability. London, England; New York, NY: Chapman and Hall.Google Scholar
Rust, R.T., Lemon, K. and Zeithaml, V.A. (2004) Return on marketing: Using customer equity to focus marketing strategy. Journal of Marketing, 68 (1), 109–127.CrossRefGoogle Scholar