Modeling, inference and risk aggregation for dependent insurance losses

家属保险损失的建模、推理和风险汇总

• 批准号: RGPIN-2019-04190
• 负责人: Côté, MariePier
• 金额: $ 1.68万
• 依托单位: Université Laval
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714002
• 关键词: Modeling; inference; risk; aggregation; dependent

Insurance companies are now increasingly interested in the detailed modeling of their policies and claims. At such level of granularity, dependence between the different components naturally arises, and must be considered to appropriately measure the overall risk. My research program focuses on the development of sound models and statistical methods to account for dependence between general insurance risks. Copula-based models are more adequately representing the dependence in multivariate data than the usual multivariate distributions. They are formed by a copula, encapsulating the dependence structure, and a marginal distribution for each of the random variable. However, high-dimensional versions of common copulas are often too restrictive in practice, and my research program aims at providing new options of flexible copulas that are interpretable through a stochastic representation. Hierarchical constructions generalizing the background risk model, which is basically a random scaling applied to a random vector, will lead to dependence structures that may exhibit asymmetries, homogeneous subvectors and have different levels of lower and upper tail dependence. I will also develop the corresponding inference procedures. As big data analysis is changing the game in the insurance industry, I will study copula models in conjunction with complex, hard-to-interpret marginal distributions built from machine learning procedures that are now available to improve the fit. The models and the corresponding inference procedure that I will develop could be applied in actuarial, hydrological or financial applications and I will make them accessible through the R Project for Statistical Computing. In a micro-level reserving framework, upon the reporting of a claim and throughout its payment process until settlement, the insurer holds a reserve to cover for the future amounts to be paid in relation to that individual claim. I will develop tools to verify or refute the assumption of independence between the claims, which is underlying individual reserving models. When a claim involves many claimants or coverages, a dependence model is needed, and I will develop an inference procedure accounting for open and closed claims in this context. This detailed modeling is intricate, but its implementation would lead to many benefits for the insurance company, and ultimately for the Canadian insurance industry and for the customers. Examples include an improved fraud detection and early identification of costly files, a reduction in claims adjuster fees and the uncovering of changes in the claim mix or the repayment process.

保险公司现在对他们的保单和索赔的详细建模越来越感兴趣。在这样的粒度级别上，不同组件之间的依赖性自然会出现，并且必须被考虑以适当地测量整体风险。我的研究项目侧重于开发合理的模型和统计方法，以解释一般保险风险之间的依赖关系。 基于Copula的模型比通常的多元分布更能充分地表示多元数据的相关性。它们由一个copula构成，封装了依赖结构，以及每个随机变量的边际分布。然而，高维版本的常见copula往往是太严格的实践中，我的研究计划的目的是提供新的选项，灵活的copula是通过随机表示解释。概括背景风险模型的层次结构（基本上是应用于随机向量的随机缩放）将导致可能表现出不对称性、同质子向量以及具有不同水平的下尾和上尾依赖性的依赖结构。我还将开发相应的推理程序。由于大数据分析正在改变保险业的游戏规则，我将结合复杂的、难以解释的边际分布来研究Copula模型，这些边际分布是从机器学习程序中构建的，现在可以用来提高拟合度。我将开发的模型和相应的推理程序可以应用于精算，水文或金融应用程序，我将通过R项目统计计算使它们可访问。 在微观层面的准备金框架中，在索赔报告和整个支付过程中，直到解决，保险公司持有一笔准备金，以支付与该个人索赔有关的未来金额。我将开发工具来验证或反驳索赔之间的独立性假设，这是潜在的个人保留模型。当一个索赔涉及许多索赔人或保险，依赖模型是必要的，我将开发一个推理过程占开放和封闭的索赔在这种情况下。这种详细的建模是复杂的，但它的实施将导致许多好处的保险公司，并最终为加拿大保险业和客户。这方面的例子包括：改进了欺诈检测和早期识别昂贵的文件，减少了索赔理算人的费用，以及发现了索赔组合或偿还过程中的变化。