Modeling, inference and risk aggregation for dependent insurance losses

保险公司现在对其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关系自然会产生，必须加以考虑才能适当地衡量总体风险。我的研究项目专注于开发合理的模型和统计方法来解释一般保险风险之间的相关性。 与通常的多变量分布相比，基于Copula的模型能更好地表示多变量数据中的相关性。它们由一个包含相关性结构的Copula和每个随机变量的边际分布形成。然而，高维版本的普通联结在实践中往往过于严格，我的研究项目旨在提供可通过随机表示解释的灵活联结的新选择。背景风险模型基本上是应用于随机向量的随机尺度，层次化结构将导致可能表现出不对称、同质子向量并且具有不同程度的下尾相关性和上尾相关性的依赖结构。我还将制定相应的推理程序。随着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，这些边际分布是通过机器学习过程构建的，现在可以用来提高匹配度。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，我将通过统计计算R项目提供这些模型和相应的推理程序。 在微观准备金框架中，在报告索赔时以及在其整个支付过程中直至结清，保险公司持有准备金，以支付与该个别索赔有关的未来数额。我将开发工具来验证或驳斥主张之间的独立性假设，这是个人保留模型的基础。当一项索赔涉及多个索赔人或承保人时，需要一个相依性模型，在这种情况下，我将开发一个考虑开放和关闭索赔的推理程序。这种详细的建模是复杂的，但它的实施将为保险公司带来许多好处，并最终为加拿大保险业和客户带来好处。这方面的例子包括改进欺诈侦查和及早查明昂贵的档案、减少索赔调整员的费用以及发现索赔组合或偿还过程中的变化。

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.