Effective experience rating for large insurance portfolios via surrogate modeling
针对大型保险组合中贝叶斯经验费率计算成本高、缺乏解析表达式的问题，提出替代模型方法，通过似然汇总统计量近似推导贝叶斯保费的解析表达式，降低计算负担并提高透明度。
Experience rating in insurance uses a Bayesian credibility model to upgrade the current premiums of a contract by taking into account policyholders' attributes and their claim history. Most data-driven models used for this task are mathematically intractable, and premiums must be obtained through numerical methods such as simulation via MCMC. However, these methods can be computationally expensive and even prohibitive for large portfolios when applied at the policyholder level. Additionally, these computations become “black-box” procedures as there is no analytical expression showing how the claim history of policyholders is used to upgrade their premiums. To address these challenges, this paper proposes a surrogate modeling approach to inexpensively derive an analytical expression for computing the Bayesian premiums for any given model, approximately. As a part of the methodology, the paper introduces a likelihood-based summary statistic of the policyholder's claim history that serves as the main input of the surrogate model and that is sufficient for certain families of distribution, including the exponential dispersion family. As a result, the computational burden of experience rating for large portfolios is reduced through the direct evaluation of such analytical expression, which can provide a transparent and interpretable way of computing Bayesian premiums.