Insurance ratemaking using a copula-based multivariate Tweedie model

The Tweedie distribution, featured with a mass probability at zero, is a convenient tool for insurance claims modeling and pure premium determination in general insurance. Motivated by the fact that an insurance policy typically provides multiple types of coverage, we propose a copula-based multivariate Tweedie regression for modeling the semi-continuous claims while accommodating the association among different types. The proposed approach also allows for dispersion modeling, resulting in a multivariate version of the double generalized linear model. We demonstrate the application in insurance ratemaking using a portfolio of policyholders of automobile insurance from the state of Massachusetts in the United States.     

基于 Tweedie 类分布的广义可加模型在车险费率厘定中的应用

分析广义线性模型和广义可加模型的理论基础和特点,从Tweedie类分布的独特视角归纳保险索赔额数据的分布规律。基于此建立了GLM—Tweedie和GAM—Tweedie索赔额拟合模型,以一组汽车保险损失数据为样本进行车险费率厘定和索赔额拟合的实证分析,识别“车、人、地”不同因素对费率不同的影响程度,助推我国车险费率厘定市场化改革精算技术的提升。     

日照时间天气指数保险的费率厘定——以长沙县早稻作物为例

天气指数保险是传统农业保险、区域产量保险的创新。选择天气指数保险探讨其费率厘定,有助于克服道德风险和逆选择,确保农业保险快速、健康地发展。粮食作物日照时间天气指数保险的费率厘定,首先要测算日照过短（或日照过长）的严重程度,计算日照过短（或日照过长）测度指标;再分析气候因素导致粮食作物减产的程度,计算气候减产率;然后利用计量经济分析方法,确立气候减产率与日照过短（或日照过长）测度指标之间的定量关系;最后根据该定量关系以及日照过短（或日照过长）测度指标的期望值,求得日照时间天气指数保险的费率。     

基于可保风险泛化的风暴潮灾害保险定价研究

提高海洋灾害的风险管理能力、降低灾害损失,是海洋强国战略实施的重要保障。在依照可保风险泛化条件辨识风暴潮灾害风险可保性的基础上,本文创新并完善了一套基于非参数估计模型的海洋灾害保险定价方法,并通过构建信度保费厘定模型计算了风暴潮灾害综合险纯费率,从费率厘定的动态调整、灾害保险体系建设等方面提出了对策建议,以期为完善海洋灾害风险管理体制提供参考。     

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

In the underwriting and pricing of nonlife insurance products, it is essential for the insurer to utilize both policyholder information and claim history to ensure profitability and proper risk management. In this paper, we apply a flexible regression model with random effects, called the Mixed Logit-weighted Reduced Mixture-of-Experts, which leverages both policyholder information and their claim history, to categorize policyholders into groups with similar risk profiles, and to determine a premium that accurately captures the unobserved risks. Estimates of model parameters and the posterior distribution of random effects can be obtained by a stochastic variational algorithm, which is numerically efficient and scalable to large insurance portfolios. Our proposed framework is shown to outperform the classical benchmark models (Logistic and Lognormal GL(M)M) in terms of goodness-of-fit to data, while offering intuitive and interpretable characterization of policyholders' risk profiles to adequately reflect their claim history.