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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: jfrees@bus.wisc.edu
Fei Huang
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, NSW 2052, Australia E-Mail: feihuang@unsw.edu.au
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: francis.hui@anu.edu.au
*
E-Mail: yumo.dong@anu.edu.au
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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

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