Frailty modelling of time-to-lapse of single policies for customers holding multiple car contracts

Corporate customers often hold multiple contracts and this might give dependence between the lapsing times of the single policies. We present a shared gamma frailty model in order to study the time-to-lapse of single car policies for customers holding multiple car contracts with the same insurance company, accounting for measured and time-dependent covariates. Customers with the highest frailty value tend to leave the company earlier than the others and finding these is a central aspect within a company’s customer relationship management strategy.We estimate conditional survival curves which illustrate the decreased survival probability of a customer after a lapse in a single car insurance policy. The individual survival curves are overestimated if the underlying association for cars with the same customer is ignored. Fitting misspecified Cox’s proportional hazards model also results in an underestimation of the standard error of the parameter estimates.