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

Abstract

While both zero-inflation and the unobserved heterogeneity in risks are prevalent issues in modeling insurance claim counts, determination of Bayesian credibility premium of the claim counts with these features are often demanding due to high computational costs associated with a use of MCMC. This article explores a way to approximate credibility premium for claims frequency that follows a zero-inflated Poisson distribution via variational Bayes approach. Unlike many existing industry benchmarks, the proposed method enables insurance companies to capture both zero-inflation and unobserved heterogeneity of policyholders simultaneously with modest computation costs. A simulation study and an empirical analysis using the LGPIF dataset were conducted and it turned out that the proposed method outperforms many industry benchmarks in terms of prediction performances and computation time. Such results support the applicability of the proposed method in the posterior ratemaking practices.

Credibility Distribution Estimation with Weighted or Grouped Observations

“…Furthermore, Landsman andMakov (1998, 1999) extended the results on the exponential family to the exponential dispersion family. The following key references are related to new developments in credibility estimation: Makov et al (1996), Christiansen and Schinzinger (2016), Tsai and Lin (2017), Gong et al (2018), Xacur and Garrido (2018), Tsai and Wu (2020), Tsai and Zhang (2019), Pitselis (2020, 2021), Youn et al (2021), Wang et al (2021), Yan and Song (2022), and Kim et al (2022).…”

Improving risk classification and ratemaking using mixture‐of‐experts models with random effects

“…Besides estimating model parameters with computational efficiency, our stochastic variational ECM algorithm also directly produces the approximated posterior distribution of random effects for each individual policyholder, which is key for a posteriori risk classification and ratemaking for future policy years. Further, while VI methods have been widely used in the machine learning community as an alternative to computationally more expensive methods, such as MCMC (Blei et al, 2017), there have been few use cases of VI in the actuarial literature (see, e.g., Gomes et al, 2021; Kim et al, 2022; Kuo, 2020). We hope our paper serves as another example to showcase the potentials of VI methods for analyzing the ever‐growing amount of data available for insurance applications.…”