Random effects are particularly useful in insurance studies, to capture residual heterogeneity or to induce cross‐sectional and/or serial dependence, opening hence the door to many applications including experience rating and microreserving. However, their nonobservability often makes existing models computationally cumbersome in a multivariate context. In this paper, it is shown that the multivariate extension to the Gamma distribution based on Wishart distributions for random symmetric positive‐definite matrices (considering diagonal terms) is particularly tractable and convenient to model correlated random effects in multivariate frequency, severity and duration models. Three applications are discussed to demonstrate the versatility of the approach: (a) frequency‐based experience rating with several policies or guarantees per policyholder, (b) experience rating accounting for the correlation between claim frequency and severity components, and (c) joint modeling and forecasting of the time‐to‐payment and amount of payment in microlevel reserving, when both are subject to censoring.

中文翻译：

---

Wishart-gamma随机效应模型及其在非人寿保险中的应用

随机效应在保险研究中特别有用，它可以捕获残余的异质性或引起横截面和/或序列依赖性，从而为许多应用打开了大门，包括经验等级和微储备。但是，它们的不可观察性通常使现有模型在多变量上下文中计算繁琐。本文表明，基于Wishart分布的随机对称正定矩阵（考虑对角项）对Gamma分布的多元扩展特别易处理，并且可以在多元频率，严重性和持续时间模型中对相关随机效应进行建模。讨论了三个应用程序以证明该方法的多功能性：（a）基于频率的经验等级，其中有多个保单或每个保单持有人的保证，