几种多元零膨胀和零修正模型的比较分析及其在保险中的应用
A comparative analysis of several multivariate zero-inflated and zero-modified models with applications in insurance
摘要：
保险中的索赔频率数据记录了在有限的时间段内保险单上的索赔数量。鉴于保险公司经营多条保险业务线，其中不同业务线上的索赔频率通常是相关的，因此具有索赔频率依赖性的多变量计数建模是必不可少的。部分由于奖惩系统的操作，汽车保险中的索赔数据通常以过多的公共零为特征。这个特征被称为多元零膨胀。在本文中，我们建立了两种方法来处理这个功能。第一种是使用多变量零膨胀模型，在该模型中，我们基于标准的多变量计数分布人为地增加公共零的概率。另一种是应用多变量零修正模型，该模型处理公共零和每行中发生的索赔数量，假设至少有一个索赔单独发生。在这两个框架下的几个模型进行了全面的比较分析，使用的数据从一家大型保险公司在西班牙的汽车保险组合。保险业中一种不太常见的情况是由于记录不完整而导致的公共零的缺失。这些数据的这一特征被称为多元零紧缩。在这种情况下，我们提出的多元零修正模型仍然有效，如第二个实证研究所示。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
