Multi-State Modelling of Customer Churn

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.

Lapse risk modeling in insurance: a Bayesian mixture approach

“…Guillen et al (2012) considers survival analysis to study how long policyholders maintain their policy after the first policy lapsing. Dong et al (2022) propose multistate modeling using multinomial logistic regression that allows specific behavior over a large number of different combinations of insurance coverage and across multiple periods. Our work is based on the experience gained from data of a specific company, in which higher cancelation rates are observed at the beginning of the contracts, decreasing after some months.…”