Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T02:05:44.970Z Has data issue: false hasContentIssue false
  • English
  • Français

MULTI-STATE MODELLING OF CUSTOMER CHURN

Published online by Cambridge University Press:  08 September 2022

Yumo Dong Open the ORCID record for Yumo Dong [Opens in a new window] ,
Edward W. Frees Open the ORCID record for Edward W. Frees [Opens in a new window] ,
Fei Huang Open the ORCID record for Fei Huang [Opens in a new window]  and
Francis K. C. Hui Open the ORCID record for Francis K. C. Hui [Opens in a new window]
Yumo Dong*
Affiliation:
Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics, Australian National University, Canberra, ACT 2601, Australia
Edward W. Frees
Affiliation:
School of Business, University of Wisconsin-Madison, Madison, WI 53706, USA Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics, Australian National University, Canberra, ACT 2601, Australia E-Mail: [email protected]
Fei Huang
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, NSW 2052, Australia E-Mail: [email protected]
Francis K. C. Hui
Affiliation:
Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics, Australian National University, Canberra, ACT 2601, Australia E-Mail: [email protected]
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Customer churn, which insurance companies use to describe the non-renewal of existing customers, is a widespread and expensive problem in general insurance, particularly because contracts are usually short-term and are renewed periodically. Traditionally, customer churn analyses have employed models which utilise only a binary outcome (churn or not churn) in one period. However, real business relationships are multi-period, and policyholders may reside and transition between a wider range of states beyond that of the simply churn/not churn throughout this relationship. To better encapsulate the richness of policyholder behaviours through time, we propose multi-state customer churn analysis, which aims to model behaviour over a larger number of states (defined by different combinations of insurance coverage taken) and across multiple periods (thereby making use of readily available longitudinal data). Using multinomial logistic regression (MLR) with a second-order Markov assumption, we demonstrate how multi-state customer churn analysis offers deeper insights into how a policyholder’s transition history is associated with their decision making, whether that be to retain the current set of policies, churn, or add/drop a coverage. Applying this model to commercial insurance data from the Wisconsin Local Government Property Insurance Fund, we illustrate how transition probabilities between states are affected by differing sets of explanatory variables and that a multi-state analysis can potentially offer stronger predictive performance and more accurate calculations of customer lifetime value (say), compared to the traditional customer churn analysis techniques.

Keywords

Commercial insurancemultinomial logistic regressionhigher-order Markovlongitudinal datatransition probability
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 3 , September 2022 , pp. 735 - 764
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

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

Alai, D.H., Arnold, S. and Sherris, M. (2015) Modelling cause-of-death mortality and the impact of cause-elimination. Annals of Actuarial Science, 9(1), 167–186.CrossRefGoogle Scholar
Antonio, K., Godecharle, E. and Van Oirbeek, R. (2016) A multi-state approach and flexible payment distributions for micro-level reserving in general insurance. Available at SSRN 2777467.CrossRefGoogle Scholar
Bettonville, C., d’Oultremont, L., Denuit, M., Trufin, J. and Van Oirbeek, R. (2021) Matrix calculation for ultimate and 1-year risk in the semi-Markov individual loss reserving model. Scandinavian Actuarial Journal, 2021(5), 380–407.CrossRefGoogle Scholar
Bolancé, C., Guillen, M. and Padilla-Barreto, A.E. (2016) Predicting probability of customer churn in insurance. International Conference on Modeling and Simulation in Engineering, Economics and Management, pp. 82–91. Springer.CrossRefGoogle Scholar
Carson, Brant, Christine Korwin-Szymanowska, O. L. (2017) Mckinsey Australia small commercial insurance consumer survey. URL: https://www.mckinsey.com/industries/ financial-services/our-insights/sme-insurance-in-australia-a-market-ripe-for-change Google Scholar
Brechmann, E. and Czado, C. (2014) Spatial modeling. In Predictive Modeling Applications in Actuarial Science: Volume 1, Predictive Modeling Techniques, p. 260.CrossRefGoogle Scholar
Brian Briggs, E.C. (2021) U.S. property & casualty and title insurance industries - 2020 full year results, Technical report, National Association of Insurance Commissioners. URL: https://content.naic.org/ Google Scholar
Brockett, P.L., Golden, L.L., Guillen, M., Nielsen, J.P., Parner, J. and Perez-Marin, A.M. (2008) Survival analysis of a household portfolio of insurance policies: How much time do you have to stop total customer defection?. Journal of Risk and Insurance, 75(3), 713–737.CrossRefGoogle Scholar
Buchardt, K. (2014) Dependent interest and transition rates in life insurance. Insurance: Mathematics and Economics, 55, 167–179.Google Scholar
Buchardt, K., Møller, T. and Schmidt, K.B. (2015) Cash flows and policyholder behaviour in the semi-Markov life insurance setup. Scandinavian Actuarial Journal, 2015(8), 660–688.CrossRefGoogle Scholar
Christiansen, M.C., Eling, M., Schmidt, J.-P. and Zirkelbach, L. (2016) Who is changing health insurance coverage? Empirical evidence on policyholder dynamics. Journal of Risk and Insurance, 83(2), 269–300.CrossRefGoogle Scholar
Cortes, C. and Mohri, M. (2003) AUC optimization vs. error rate minimization. In Advances in Neural Information Processing Systems, Vol. 16.Google Scholar
De Bock, K.W. and Van den Poel, D. (2011) An empirical evaluation of rotation-based ensemble classifiers for customer churn prediction. Expert Systems with Applications, 38(10), 12293–12301.CrossRefGoogle Scholar
Devriendt, F., Berrevoets, J. and Verbeke, W. (2021) Why you should stop predicting customer churn and start using uplift models. Information Sciences, 548, 497–515.CrossRefGoogle Scholar
Devriendt, S., Antonio, K., Reynkens, T. and Verbelen, R. (2021) Sparse regression with multi-type regularized feature modeling. Insurance: Mathematics and Economics, 96, 248–261.Google Scholar
Dong, Y., Frees, E.W. and Huang, F. (2022) Deductible costs for bundled insurance contracts. Available at SSRN 4020299.CrossRefGoogle Scholar
Fong, J.H., Shao, A.W. and Sherris, M. (2015) Multistate actuarial models of functional disability. North American Actuarial Journal, 19(1), 41–59.CrossRefGoogle Scholar
Frees, E.W. (2004) Longitudinal and Panel Data: Analysis and Applications in the Social Sciences. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Frees, E.W., Bolancé, C., Guillen, M. and Valdez, E.A. (2021) Dependence modeling of multivariate longitudinal hybrid insurance data with dropout. Expert Systems with Applications, 185, 115552.CrossRefGoogle Scholar
Frees, E.W., Lee, G. and Yang, L. (2016) Multivariate frequency-severity regression models in insurance. Risks, 4(1), 4.CrossRefGoogle Scholar
Guelman, L., Guillén, M. and Pérez-Marn, A.M. (2012) Random forests for uplift modeling: an insurance customer retention case. International Conference on Modeling and Simulation in Engineering, Economics and Management, pp. 123–133. Springer.CrossRefGoogle Scholar
Guillen, M., Nielsen, J.P., Scheike, T.H. and Pérez-Marn, 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
Guillen, M., Nielsen, J. and Pérez-Marn, A. (2009) Cross buying behaviour and customer loyalty in the insurance sector. EsicMarket, 132, 77–105.Google Scholar
Guillen, M., Parner, J., Densgsoe, C. and Perez-Marin, A.M. (2003) Using logistic regression models to predict and understand why customers leave an insurance company. In Intelligent and Other Computational Techniques in Insurance: Theory and Applications, pp. 465–490. World Scientific.CrossRefGoogle Scholar
Günther, C.-C., Tvete, I.F., Aas, K., Sandnes, G.I. and Borgan, Ø. (2014) Modelling and predicting customer churn from an insurance company. Scandinavian Actuarial Journal, 2014(1), 58–71.CrossRefGoogle Scholar
Gupta, S., Lehmann, D.R. and Stuart, J.A. (2004) Valuing customers. Journal of Marketing Research, 41(1), 7–18.CrossRefGoogle Scholar
Haberman, S. and Pitacco, E. (2018) Actuarial Models for Disability Insurance, Abingdon, Oxfordshire: Routledge.CrossRefGoogle Scholar
Hand, D.J. and Till, R.J. (2001) A simple generalisation of the area under the ROC curve for multiple class classification problems. Machine Learning, 45(2), 171–186.CrossRefGoogle Scholar
He, H. and Ma, Y. (2013) Imbalanced Learning: Foundations, Algorithms, and Applications. Hoboken, New Jersey: John Wiley & Sons.CrossRefGoogle Scholar
He, Y., Xiong, Y. and Tsai, Y. (2020) Machine learning based approaches to predict customer churn for an insurance company. 2020 Systems and Information Engineering Design Symposium (SIEDS), pp. 1–6. IEEE.Google Scholar
Holtrop, N., Wieringa, J.E., Gijsenberg, M.J. and Verhoef, P.C. (2017) No future without the past? predicting churn in the face of customer privacy. International Journal of Research in Marketing, 34(1), 154–172.CrossRefGoogle Scholar
Hürlimann, W. (2015) A simple multi-state gamma claims reserving model. International Journal of Contemporary Mathematical Sciences, 10(2), 65–77.CrossRefGoogle Scholar
Kuhn, M. (2021) caret: Classification and Regression Training. R package version 6.0-88. URL: https://CRAN.R-project.org/package=caret Google Scholar
Kwon, H.-S. and Jones, B.L. (2006) The impact of the determinants of mortality on life insurance and annuities. Insurance: Mathematics and Economics, 38(2), 271–288.Google Scholar
Kwon, H.-S. and Jones, B.L. (2008) Applications of a multi-state risk factor/mortality model in life insurance. Insurance: Mathematics and Economics, 43(3), 394–402.Google Scholar
Kwon, H.-S. and Nguyen, V.H. (2019) Analysis of cause-of-death mortality and actuarial implications. Communications for Statistical Applications and Methods, 26(6), 557–573.CrossRefGoogle Scholar
Leeper, T.J. (2017) Interpreting regression results using average marginal effects with r’s margins. Reference Manual, 32.Google Scholar
Lemmens, A. and Croux, C. (2006) Bagging and boosting classification trees to predict churn. Journal of Marketing Research, 43(2), 276–286.CrossRefGoogle Scholar
Loisel, S., Piette, P. and Tsai, C.-H.J. (2021) Apply ing economic measures to lapse risk management with machine learning approaches. ASTIN Bulletin: The Journal of the IAA, 51(3), 839–871.CrossRefGoogle Scholar
Madigan, D., Genkin, A., Lewis, D.D. and Fradkin, D. (2005) Bayesian multinomial logistic regression for author identification. AIP Conference Proceedings, Vol. 803, pp. 509–516. American Institute of Physics.CrossRefGoogle Scholar
Min, H. and Zhou, G. (2002) Supply chain modeling: Past, present and future. Computers & Industrial Engineering, 43(1–2), 231–249.CrossRefGoogle Scholar
Morrison, D.G. (1969) On the interpretation of discriminant analysis. Journal of marketing research, 6(2), 156–163.CrossRefGoogle Scholar
Neslin, S.A., Gupta, S., Kamakura, W., Lu, J. and Mason, C.H. (2006) Defection detection: Measuring and understanding the predictive accuracy of customer churn models. Journal of Marketing Research, 43(2), 204–211.CrossRefGoogle Scholar
Norberg, R. (2013) Optimal hedging of demographic risk in life insurance. Finance and Stochastics, 17(1), 197–222.CrossRefGoogle Scholar
Okine, A.N.-A., Frees, E.W. and Shi, P. (2022) Joint model prediction and application to individual-level loss reserving. ASTIN Bulletin: The Journal of the IAA, 52(1), 91–116.CrossRefGoogle Scholar
Okongwu, U., Lauras, M., François, J. and Deschamps, J.-C. (2016) Impact of the integration of tactical supply chain planning determinants on performance. Journal of Manufacturing Systems, 38, 181–194.CrossRefGoogle Scholar
Orr, J. (2007) A simple multi-state reserving model. ASTIN, Colloqiua Orlando edition. URL: https://www.actuaries.org/ASTIN/Colloquia/Orlando/Papers/Orr.pdf Google Scholar
Pendharkar, P.C. (2009) Genetic algorithm based neural network approaches for predicting churn in cellular wireless network services. Expert Systems with Applications, 36(3), 6714–6720.CrossRefGoogle Scholar
Pritchard, D. (2006) Modeling disability in long-term care insurance. North American Actuarial Journal, 10(4), 48–75.CrossRefGoogle Scholar
Scriney, M., Nie, D. and Roantree, M. (2020) Predicting customer churn for insurance data. International Conference on Big Data Analytics and Knowledge Discovery, pp. 256–265. Springer.CrossRefGoogle Scholar
Shi, P., Fung, G.M. and Dickinson, D. (2022) Assessing hail risk for property insurers with a dependent marked point process. Journal of the Royal Statistical Society: Series A (Statistics in Society). 185(1), 302–328.Google Scholar
Shi, P. and Yang, L. (2018) Pair copula constructions for insurance experience rating. Journal of the American Statistical Association, 113(521), 122–133.CrossRefGoogle Scholar
Simchi-Levi, D., Kaminsky, P., Simchi-Levi, E. and Shankar, R. (2008) Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies. New York: Tata McGraw-Hill Education.Google Scholar
Staudt, Y. and Wagner, J. (2018) What policyholder and contract features determine the evolution of non-life insurance customer relationships? International Journal of Bank Marketing. 36(6), 1098–1124.CrossRefGoogle Scholar
Venables, W.N. and Ripley, B.D. (2002) Modern Applied Statistics with S, 4th ed. New York: Springer. ISBN 0-387-95457-0. URL: https://www.stats.ox.ac.uk/pub/MASS4/ CrossRefGoogle Scholar
Wu, X.-Z. and Zhou, Z.-H. (2017) A unified view of multi-label performance measures. International Conference on Machine Learning, pp. 3780–3788. PMLR.Google Scholar
Yeo, A.C., Smith, K.A., Willis, R.J. and Brooks, M. (2001) Modeling the effect of premium changes on motor insurance customer retention rates using neural networks. International Conference on Computational Science, pp. 390–399. Springer.Google Scholar
Zhu, Z., Li, Z., Wylde, D., Failor, M. and Hrischenko, G. (2015) Logistic regression for insured mortality experience studies. North American Actuarial Journal, 19(4), 241–255.CrossRefGoogle Scholar
Supplementary material: PDF

Dong et al. supplementary material

Dong et al. supplementary material

Download Dong et al. supplementary material(PDF)
PDF 377.7 KB