Actuarial ratemaking is usually performed at product and guarantee level, meaning that each product and guarantee is considered in isolation. Moreover, independence between policyholders is generally assumed. In this paper, we propose a multivariate Poisson mixture, with random effects correlated using a hierarchical structure, to accommodate for the dependence that may exist between unobserved risk factors across Home and Motor insurance and between policyholders from the same household. The hierarchical structure accounts for the fact that Home insurance covers the whole household, whereas Motor insurance policies are subscribed by specific policyholders within the household. The model allows to periodically correct the a priori expected claim frequencies using the reported number of claims in any of the considered products. Applications show that the impact of the number of claims reported in Motor insurance on the number of claims expected in Home insurance is larger than the other way around. Moreover, an out-of-sample analysis validates an improved predictive power. Also, the model allows to identify more rapidly the riskiest households.

中文翻译：

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使用多元可信度在家庭层面加入家庭和汽车保险

精算费率制定通常在产品和保证级别进行，这意味着每个产品和保证都被单独考虑。此外，通常假设保单持有人之间的独立性。在本文中，我们提出了一种多元泊松混合，其中随机效应使用分层结构进行关联，以适应家庭和汽车保险中未观察到的风险因素之间以及来自同一家庭的保单持有人之间可能存在的依赖性。等级结构说明了家庭保险覆盖整个家庭的事实，而汽车保险单则由家庭内的特定投保人订阅。该模型允许使用任何考虑的产品中报告的索赔数量定期更正先验预期的索赔频率。应用表明，汽车保险中报告的索赔数量对家庭保险中预期索赔数量的影响大于相反。此外，样本外分析验证了改进的预测能力。此外，该模型允许更快地识别风险最高的家庭。