Modeling dependence between individual risks in property & casualty loss reserving

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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.