论文标题
对几个多元零膨胀和零改装模型的比较分析，并使用保险中的应用
A comparative analysis of several multivariate zero-inflated and zero-modified models with applications in insurance
论文作者
论文摘要
保险记录中的索赔频率数据在有限的时间内保险单上的索赔数量。鉴于保险公司在多个保险业务中运营，在不同的业务上的索赔频率通常是相关的，因此对索赔频率的多元计数建模至关重要。部分原因是奖金 - 麦卢斯系统的运行，汽车保险中的索赔数据通常以过量的零零为特征。此功能称为多元零通气。在本文中，我们建立了两种处理此功能的方法。首先是使用多变量零膨胀模型，在该模型中，我们根据标准多元计数分布人为地增加了共同零的概率。另一个是应用多元零修饰的模型，该模型涉及共同的零和每行索赔的数量，鉴于至少一个索赔是单独发生的。使用西班牙一家主要保险公司的汽车保险投资组合的数据对这两个框架下的几个模型进行了全面的比较分析。保险中不太普遍的情况是由于记录不完整而没有一些常见的零。这些数据的此功能称为多元零驱动。在这种情况下，我们提出的多元零修饰模型仍然有效，如第二次实证研究所示。
Claim frequency data in insurance records the number of claims on insurance policies during a finite period of time. Given that insurance companies operate with multiple lines of insurance business where the claim frequencies on different lines of business are often correlated, multivariate count modeling with dependence for claim frequency is therefore essential. Due in part to the operation of bonus-malus systems, claims data in automobile insurance are often characterized by an excess of common zeros. This feature is referred to as multivariate zero-inflation. In this paper, we establish two ways of dealing with this feature. The first is to use a multivariate zero-inflated model, where we artificially augment the probability of common zeros based on standard multivariate count distributions. The other is to apply a multivariate zero-modified model, which deals with the common zeros and the number of claims incurred in each line, given that at least one claim occurs separately. A comprehensive comparative analysis of several models under these two frameworks is conducted using the data of an automobile insurance portfolio from a major insurance company in Spain. A less common situation in insurance is the absence of some common zeros resulting from incomplete records. This feature of these data is known as multivariate zero-deflation. In this case, our proposed multivariate zero-modified model still works, as shown by the second empirical study.
