Essays on Claims Modelling, Customer Churn Analysis, and Customer Valuation in General Insurance

Abstract

This thesis presents three essays themed around the topics of claims modelling, customer churn analysis, and customer valuation in general insurance. Chapter 2 studies multivariate claims modelling with combined deductibles, Chapter 3 explores multi-state customer churn analysis, and Chapter 4 focuses on cost-based customer lifetime value (CLV) models. While each chapter offers a unique and innovative contribution to the existing literature on the aforementioned topics, the research problems tackled in all three chapters are of broad and referential significance to general insurance companies.

In Chapter 2, we study the dependence modelling of multivariate insurance claims with the consideration of a combined deductible. Without combined deductibles, it is straightforward to value bundled insurance contracts as the sum of contracts from each supporting coverage. However, with combined deductibles, assumptions about the relationships among coverages become important. To demonstrate this importance, we evaluate the cost of combined deductibles under dependence via copulas, and show the impact of dependence modelling using three applications (commercial insurance, reinsurance, and personal insurance). This chapter also examines a range of dependence parameters, marginal distributions, and copulas in the simulation study, and supplements the findings from the simulation study with several theoretical propositions.

Chapter 3 explores multi-state customer churn analysis in general insurance. Traditionally, customer churn analyses have employed models that 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 understand policyholder behaviours in real business relationships, we propose a multi-state customer churn analysis that aims to model customer behaviour over a larger number of states (defined by different combinations of insurance policies taken) and across multiple periods. Using multinomial logistic regression (MLR) with a second-order Markov assumption, we demonstrate how a policyholder's transition history is associated with their decision-making, whether that be to retain the current set of policies, churn, or to add/drop a policy or coverage.

In Chapter 4, we introduce a CLV modelling framework suitable for the insurance industry. Traditional CLV models focus on modelling revenues and churn but often neglect modelling costs to serve customers. In the insurance industry, a major cost component is insurance claims, which are highly variable and can be extremely large in size. Existing CLV models are not suitable for the insurance industry because they do not capture costs adequately and ignore the association between costs (claims) and the likelihood to churn. To bridge this gap, we introduce a novel cost-based CLV modelling framework. Utilising a Tweedie regression approach for claims, combined with shared random effects between the claims and churn processes, our model successfully captures unobserved and correlated heterogeneity in claims and churn risks across customers. Applying our proposed model to commercial insurance data, we illustrate how this model can capture latent associations between claims and churn tendencies, enhance predictive CLV performance, and bring novel managerial insights into CLV analyses.