Dependence Modeling in Insurance and Finance: Estimation, Ratemaking and Reserving

本程序专注于保险中遇到的高度非连续变量与信用风险之间的相关性建模，例如二元变量、计数变量或正变量(潜在截尾，或点质量为零)，或有界变量。这些数据可以是横截面的，也可以是纵向的，通常是用高维协变量观察到的。例如，在非寿险中，人们通常观察到每个人的索赔计数和一个正变量(总索赔严重性)；在信用风险中，人们观察到一个二元指标(违约指标)，以及违约情况下的给定违约损失(LGD)，它的界限是0和1，可能有概率分布。在这两种应用中，响应变量之间的相关性对于风险管理是必不可少的，但由于其非连续特性，其建模具有挑战性。尽管数据功能相似，但这两个社区仍然以某种方式脱节，并面临着相似的挑战。特别是，尽管最近这两个领域都采用了机器学习(ML)技术，但其中许多技术也有自己的缺点。我的长期目标是：i)通过引入在这两个领域都有用的新方法以及适当的技术转让，拉近这两个领域的距离；ii)在传统统计模型和用于相关性建模的机器学习(ML)技术之间架起一座桥梁。更确切地说，我的具体目标如下：-将随机效应模型的适用性扩展到新的背景和新的应用中，随机效应模型是保险和信用风险中用于相关性建模的强大的(统计)模型家族，使ML方法与金融数据的特征相协调，并缓解目前精算和信用风险文献中提出的现有ML方法的缺点。特别是，我将考虑适用于多变量和/或纵向数据的最大似然方法，以便能够有效地考虑相关性。-从经验和理论上直面传统方法和ML方法。特别是，我将试图回答一个长期的辩论，即信用违约和相关的亏损违约之间是否以及如何考虑相关性，并寻找新的、与经济相关的、考虑潜在相关性的模型选择标准。该计划的预期影响是：i)通过培训合格的研究生和合作，弥合学术界和工业界之间的差距；ii)通过统一的研究计划，拉近工业界和学术界精算和信用风险领域的距离。Iii)通过对传统方法和ML方法的仔细分析和比较，有助于更好地理解ML方法在零售金融/保险领域的真正力量。

This program focuses on dependence modelling between highly non-continuous variables encountered in Insurance and credit risk, such as binary, count or positive variables (with potentially censoring, or point mass at zero), or bounded variables. Such data can be available either crosssectionally, or longitudinally, and are typically observed with high--dimensional covariates. For instance, in non-life insurance, one typically observes, for each individual, a claim count and a positive variable (total claim severity); in credit risk, one observes a binary indicator (the default indicator), as well as the loss--given-default (LGD) in case of default, which is bounded by 0 and 1, with possibly probability masses at bounds. In both applications, the dependence between the response variables is essential for risk management but their modeling is challenging due to the non-continuous feature. Despite the similarities of the data features, the two communities remain somehow disconnected, and face similar challenges. In particular, although recently both domains have embraced machine learning (ML) techniques, many of them have also their own downsides. My long-term objective is to i) bring the two fields closer, through the introduction of new methodologies useful in both fields, as well as appropriate technology transfer, and ii) bridge the link between traditional statistical models and machine learning (ML) techniques for dependence modelling. More precisely, my detailed objectives are as follows: -Extend the applicability of random effect models, which is a powerful family of (statistical) models for dependence modeling in insurance and credit risk, to new settings and new applications.  -Reconcile ML methods with the characteristics of financial data, and mitigate the shortcomings of existing ML methods currently proposed in the actuarial and credit risk literature. In particular I will consider ML methods that are suitable for multivariate and/or longitudinal data, so that dependence can be effectively taken into account. -Confront traditional approaches and ML methods, both empirically, and theoretically. In particular I will try to answer a long-term debate on whether and how dependence should be accounted for between credit default and the associated loss-given default, and look for new, economically-relevant model selection criteria that account for potential dependence. The expected impacts of this program is i) through training of qualified graduate students and collaboration, bridging the gap between academia and industry, ; ii) through a unified research program, bringing closer the actuarial and credit risk domains, both in industry and academia. iii) through careful analysis and comparison of both traditional and ML methods, contributing to a better understanding of the true power of ML methods for retail financial/insurance.