保险索赔金额的上尾建模：来自丹麦火灾保险数据的证据

Modelling the Upper Tail of Insurance Claim Amount: Evidence from Danish Fire Insurance Data

摘要: 为了对保险索赔数据进行建模，即找到最适合的分布，本文使用最大似然框架对丹麦火灾保险数据进行建模和分析，并在幂律分布，对数正态分布和威布尔分布这三种候选分布中找到每组数据的最适合分布。研究发现，建筑损失组数据符合对数正态分布；内容物损失组数据符合对数正态分布；利润损失组的数据很好地拟合了幂律分布，而总损失组的数据也很好地符合幂律分布。此外，我们还证明了下界的估计影响模型参数的估计和用于测试分布的p值。最后，我们使用拟合分布模型来获得相应的VaR，并将其与经验VaR进行比较，结果相似。这也意味着最大似然框架有助于保险索赔数据的建模。

Abstract: In order to model the insurance claim data, that is, to find the most suitable distribution, this paper uses the maximum likelihood framework to model and analyze the Danish fire insurance data, and finds the most suitable distribution for each group of data among the three candidate distributions of Power law distribution, Lognormal distribution and Weibull distribution. It is found that the data of Building group is well fitted by Lognormal distribution; the data of Contents group is well fitted by Lognormal distribution; The data of Profits group is well fitted by the Power law distribution, and the data of Total group is well fitted by the Power law distribution. Moreover, we also prove that the estimation of the lower bound affects the estimation of the model parameters and the p-values used to test the distributions. Finally, we use the fitted distribution model to obtain the corresponding VaR and compare it with the empirical VaR, and the results are similar. This also means that the maximum likelihood framework is helpful to the modeling of insurance claim data.