Improving detections of serial dynamics for longitudinal actuarial data with underwriting-controlled testing

Abstract

Longitudinal actuarial data, where policyholders' claims are recorded over multiple years, offer valuable insights for pricing and reserving. However, standard modeling approaches typically assume no serial dynamics in conditional claim distributions over time. Such an assumption is difficult to validate given that most non-life insurance products are short-term, yielding data from only a few years. Recent diagnostic methods can detect serial dynamics but do not distinguish between changes induced by endogenous underwriting standards (e.g., renewal and pricing policies favoring low-risk policyholders) and genuine, exogenous temporal shifts (e.g., evolving socioeconomic environment). In this paper, we develop underwriting-controlled serial dynamic tests for longitudinal actuarial data. By applying an inverse-probability-weighted estimation approach, we adjust for underwriting effects and thus detect the true underlying serial dynamics. We propose tests based on three metrics, parameter difference, prediction bias, and prediction loss, enabling both statistical and economic interpretations of dynamic changes. Simulation studies show that our tests avoid false detections caused by underwriting effects. An analysis using European automobile insurance data illustrates how our approach offers deeper insights into when and why serial dynamics emerge.