Lapse risk modelling in insurance: a Bayesian mixture approach

TL;DR

This paper introduces a Bayesian mixture survival model to accurately capture the complex lapse behavior in life insurance, addressing high censuring rates and heterogeneous lapse patterns with scalable inference methods.

Contribution

It develops a novel Bayesian mixture approach for modeling lapse times, incorporating censuring and heterogeneity, with efficient inference techniques suitable for large datasets.

Findings

Model effectively captures initial high lapse rates and their decrease over time.

Scalable inference methods enable analysis of over a million clients.

Simulated studies demonstrate robustness under high censuring conditions.

Abstract

This paper focuses on modelling surrender time for policyholders in the context of life insurance. In this setup, a large lapse rate at the first months of a contract is often observed, with a decrease in this rate after some months. The modelling of the time to cancellation must account for this specific behaviour. Another stylised fact is that policies which are not cancelled in the study period are considered censored. To account for both censuring and heterogeneous lapse rates, this work assumes a Bayesian survival model with a mixture of regressions. The inference is based on data augmentation allowing for fast computations even for data sets of over a million clients. Moreover, scalable point estimation based on EM algorithm is also presented. An illustrative example emulates a typical behaviour for life insurance contracts and a simulated study investigates the properties of the proposed model. In particular, the observed censuring in the insurance context might be up to 50% of the data, which is very unusual for survival models in other fields such as epidemiology. This aspect is exploited in our simulated study.