Modeling dependence between individual risks in property & casualty loss reserving

如今，人们越来越关注个性化保费和基于使用情况的保险，保险公司正在利用物联网和机器学习来开发更精细的个人风险概况。准备金构成了财产保险公司的大部分责任。然而，如果你仔细研究一下今天普遍使用的损失准备金技术，就会发现，它们陷入了依赖于20世纪处理综合风险的方法的困境，无法适应当前的保险趋势。对单个风险进行分组通常会导致异质性问题。此外，经典的保留方法往往是在风险之间独立的假设下确定的。然而，风险在实践中是相互关联的，需要考虑这种依赖关系。我的研究计划的中心长期愿景是更好地理解个体风险内部和之间的依赖关系，并评估外生因素对财产保险损失准备金的影响。为了实现我的总体目标，我的研究计划将在以下两个主要途径下进行总结。(1)精细创新的颗粒依赖性模型方法：被保险人的同一次事故将同时影响不同的保险范围。为了捕捉个体风险内部和个体风险之间的依赖关系，我将设计分层的联结模型。此外，我将使用随机效应来捕获可能来自不可观察的个体风险特征的依赖性。例如，无论索赔类型如何，一些被保险人倾向于比其他人索赔更多。(2)在损益预提中纳入外生因素：影响损益公司负债的因素有很多。例如，与长期负债有关的通货膨胀是一个主要的风险来源，并可能严重影响对未来赔偿（例如索赔结算）和费用（例如诉讼费）的适当估计。将这些外生因素纳入损失准备金将为精算文献提供严谨的理论结果，并为行业的实际需求提供有趣的答案。影响与意义：本研究项目将更加重视颗粒依赖性，提高对外源因素对储备文献影响的认识。在这个研究项目中研究的统计方法将允许新技术的发展，这将对科学界产生影响。对于从业者来说，由于对依赖结构和外生因素影响的更好理解，拟议的研究计划将对财产保险公司产生明显和实际的影响，并将帮助他们满足即将出台的国际财务报告准则（IFRS 17）的规定，从而更好地评估偿付能力风险。这将产生积极的经济和社会影响，因为由于保险公司偿债能力比率的提高，被保险人将得到更好的服务和更多的保护。

Today there is an increasing focus on personalized premiums and usage-based coverage, insurers are leveraging Internet of Things, and machine learning to develop more granular individual risk profiles. Reserves comprise most of the liabilities of a property & casualty (P&C) company. Yet if you examine loss-reserving techniques commonly used today, they are mired in reliance on 20th century methods that work with aggregated risks, and non-adapted to the current insurance trends. Grouping individual risks usually leads to heterogeneity issues. Moreover, classical reserving methods are often determined under an assumption of independence between risks. However, risks are related to each other in practice and this dependence needs to be considered. The central long-term vision of my research program is to better understand the dependence within and between individual risks and evaluate the impact of exogenous factors on the P&C loss reserving. To achieve my overarching objective, my research program will be conducted under two main avenues summarized below. (1) Elaborate innovative approaches to model granular dependence: A same accident from the insured will impact different coverages at the same time. To capture this dependence within and between individual risks, I will design hierarchical copula models. Further, I will use random effects to capture the dependence that may come from unobservable individual risk characteristics. For example, some insureds tend to claim more than others, regardless of the type of claim. (2) Include exogenous factors in P&C loss reserving: There are many factors that can influence the liabilities of a P&C company. For example, inflation associated with long-term liabilities represents a major risk source and can considerably impact the adequate estimation of the future indemnities (e.g. claim settlement) and the expenses (e.g. court costs). Incorporating these exogenous factors in loss reserving will provide rigorous theoretical results to the actuarial literature and interesting answers to the practical needs of the industry. IMPACT AND SIGNIFICANCE: The proposed research program will put more emphasis on granular dependence and will raise awareness on the impact of exogenous factors in the reserving literature. The statistical approaches studied in this research program will allow the development of new techniques that will have an impact in the scientific community. For practitioners, thanks to a better understanding of the structure of dependence and exogenous factors impact, the proposed research program will have palpable and practical implications for P&C insurance companies and will help them meet the upcoming International Financial Reporting Standard (IFRS 17) regulations, leading to a better solvency risk assessment. This will generate a positive economical and societal impact, as the insured will be better served and more protected, thanks to this improved solvency ratio of the insurance company.