一个多年期微观集合风险模型
On a Multi-Year Microlevel Collective Risk Model
摘要：
对于典型的保险组合，短时间（通常为一年）的索赔过程的特征在于观察索赔频率以及相关的索赔严重程度。集体风险模型将这一投资组合描述为索赔金额总和的随机和。在经典的框架中，为了简单起见，索赔频率和索赔严重性被假设为相互独立的。然而，人们越来越倾向于放宽这一独立性假设，因为这对实际的保险费率制定更现实、更有用。虽然公共线程已经在单个时期内捕获了频率和聚合严重性之间的依赖关系，但Oh等人的工作（2020 a）提供了一个有趣的扩展，以捕获个体严重性之间的依赖关系。在本文中，我们扩展这些工作的框架内，我们有一个组合的微观频率和严重性多年。这使我们能够开发一个因子Copula模型框架，该框架可以捕获多年来索赔频率和索赔严重程度之间的各种类型的依赖关系。因此，这是一个明确的延伸，早期的工作，一年依赖的频率-严重程度模型和随机效应模型捕捉序列相关的索赔。我们专注于使用一个家庭的椭圆copula模型的依赖性的结果。本文进一步介绍了如何校准所提出的模型，使用说明性的索赔数据产生的新加坡保险公司。估计结果提供了强有力的证据，我们的模型捕获的所有形式的依赖关系。
英文摘要：
For a typical insurance portfolio, the claims process for a short period, typically one year, is characterized by observing frequency of claims together with the associated claims severities. The collective risk model describes this portfolio as a random sum of the aggregation of the claim amounts. In the classical framework, for simplicity, the claim frequency and claim severities are assumed to be mutually independent. However, there is a growing interest in relaxing this independence assumption which is more realistic and useful for the practical insurance ratemaking. While the common thread has been capturing the dependence between frequency and aggregate severity within a single period, the work of Oh et al. (2020a) provides an interesting extension to the addition of capturing dependence among individual severities. In this paper, we extend these works within a framework where we have a portfolio of microlevel frequencies and severities for multiple years. This allows us to develop a factor copula model framework that captures various types of dependence between claim frequencies and claim severities over multiple years. It is therefore a clear extension of earlier works on one-year dependent frequency-severity models and on random effects model for capturing serial dependence of claims. We focus on the results using a family of elliptical copulas to model the dependence. The paper further describes how to calibrate the proposed model using illustrative claims data arising from a Singapore insurance company. The estimated results provide strong evidence of all forms of dependencies captured by our model.
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。
