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Wishart-gamma random effects models with applications to nonlife insurance

机译：Wishart-Gamma随机效果模型与应用到非生命保险

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摘要

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.
机译：随机效应在保险研究中特别有用，以捕获残留的异质性或诱导横截面和/或串行依赖，因此在包括经验额定值和微生物的许多应用中的门口。然而，它们的非角色操作性通常使现有模型在多变量上下文中计算地繁琐。在本文中，示出了基于随机对称正面矩阵的Wishart分布（考虑对角线术语）的WAMMA分布的多元扩展是特别易行的，方便的是在多变频，严重程度和持续时间模型中模拟相关的随机效果。讨论了三个申请以证明该方法的多功能性：（a）基于频率的经验评级，每个保单持有人的若干政策或保证，（b）索赔频率和严重性组成部分之间的相关性的经验账户，以及（c）联合建模之间的相关性核算当两者都受到审查时，预测MicroLevel保留的暂时支付和金额的预测。

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