Jae Youn Ahn
Ewha Womans University
Room: M3 3127
State-Space Representations of Negative-Binomial INGARCH Models for Insurance Ratemaking
Abstract: Integer-valued generalized autoregressive conditional heteroskedastic (INGARCH) models are a popular framework for modeling serial dependence in count time series, with the dynamics specified through a recursion for the conditional mean. While convenient for modeling, prediction, and estimation, their standard formulation can be restrictive in insurance applications, where explanatory variables are essential for capturing policyholder heterogeneity. Moreover, a suitable notion of stationarity is particularly useful for ratemaking, given the short time series typically available in insurance panels. These requirements are difficult to reconcile in the classical INGARCH formulation because the conditional mean plays two roles simultaneously: it governs the temporal evolution of the process and determines the scale of the observations. To address these issues, we propose a heterogeneous negative-binomial INGARCH(1,1) model for insurance ratemaking, in which the predictive mean is decomposed into a time-varying a priori rate and a baseline conditional mean. The a priori rate accommodates time-varying heterogeneity, while the baseline conditional mean preserves the affine INGARCH recursion. Since time-varying heterogeneity makes stationarity of the observed count process inappropriate, weak stationarity is instead formulated at the level of the latent state process through an equivalent state-space model representation. The practical implementation of the model is illustrated using panel insurance data, highlighting its applicability to predictive analysis in property and casualty insurance ratemaking. This presentation is based on the joint work with Hong Ben Lim (CUHK) and Mario Wüthrich (ETH).