A simple Bayesian state-space model for the collective risk model

Abstract

The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, macro-level catastrophic risk forecasting, as well as operational risk in banking regulation. This model, which is initially designed for cross-sectional data, has recently been adapted to a longitudinal context to conduct both a priori and a posteriori ratemaking, through the introduction of random effects. However, so far, the random effect(s) is usually assumed static due to computational concerns, leading to predictive premium that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effect process. The model is based on Bayesian state-space models. It is associated with the simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. Real data application to auto insurance is proposed to show the performance of our method.

Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

“…It means there is no room for evolution of the unobserved risk characteristics of a policyholder over time under this model, which is somewhat unrealistic. While there are some research work focused on the use of dynamic random effects for determination of credibility premium (Ahn et al 2021b;Pinquet 2020), calibration and prediction of dynamic random effects models are often computationally intensive and intractable. Therefore, as a direction for future research, one can expand the class of variational family so that impacts of dynamic random effects can be incorporated in the posterior premium calculation.…”