  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.
