Regularized matrix exponential distributions and lapse modeling: the case of the French credit life insurance market

Abstract In this paper, we investigate how policyholder information and broader economic conditions jointly influence the duration of credit life insurance contracts in the French market. Employing a proportional-intensities regression framework built on inhomogeneous phase-type distributions, we capture the way covariates shape the distribution of policy lifetime until a lapse occurs. The model is estimated via a specialized expectation-maximization algorithm, adapted to handle censored data, covariates, and feature selection through shrinkage. Our analysis of real-world data shows that different policyholder attributes and economic factors can significantly alter lapse behavior, with effects varying across insurance products, individuals, and economic cycles. These findings highlight the importance of integrating both individual-level and macroeconomic indicators in lapse risk assessment, ultimately informing more accurate pricing and allowing for improved risk management strategies.