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状况。准备金包括财产和意外伤害（P&C）公司的大部分负债。然而，如果你研究一下今天常用的损失准备金技术，你会发现它们依赖于20世纪世纪处理综合风险的方法，而且不适应当前的保险趋势。单一的风险通常会导致异质性问题。此外，经典的准备金方法往往是在风险之间相互独立的假设下确定的。然而，在实践中，风险是相互关联的，需要考虑这种依赖性。 我的研究计划的中心长期愿景是更好地了解内部和个体风险之间的依赖关系，并评估外部因素对P&C损失准备金的影响。为了实现我的总体目标，我的研究计划将在下面总结的两个主要途径进行。 (1)详细阐述创新方法来建模粒度依赖性：被保险人的同一事故将同时影响不同的承保范围。为了捕捉个体风险内部和个体风险之间的这种依赖关系，我将设计分层copula模型。此外，我将使用随机效应来捕捉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，一些被保险人往往比其他人索赔更多。 (2)在财产险损失准备中包括外生因素：有许多因素会影响财产险公司的负债。例如，与长期负债有关的通货膨胀是一个主要的风险来源，可能对未来赔偿（如理赔）和费用（如诉讼费）的适当估计产生很大影响。将这些外生因素纳入到损失准备金中，将为精算文献提供严格的理论结果，并为行业的实际需求提供有趣的答案。 影响和意义：建议的研究计划将更加重视粒度依赖，并将提高认识的影响，外生因素的保留文献。在这项研究计划中研究的统计方法将允许新技术的发展，将在科学界产生影响。对于从业者来说，由于更好地了解依赖结构和外生因素的影响，拟议的研究计划将对P&C保险公司产生明显的实际影响，并将帮助他们满足即将到来的国际财务报告准则（IFRS 17）法规，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付能力的提高，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.