A Dynamic Credibility Model with Self-Excitation and Exponential Decay

This paper proposes a dynamic credibility model for claim count that extends the benchmark Poisson generalized linear models (GLM) by incorporating self-excitation and exponential decay features from Hawkes processes. Under the proposed model, a recent claim has a bigger impact on the credibility premium than an outdated claim. Empirical results show that the proposed model outperforms the Poisson GLM in both in-sample goodness-of-fit and out-of-sample prediction.