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This paper summarizes the use of Extreme Value Theory (EVT) for modeling large insurance claims, particularly within reinsurance, where managing tail risk is paramount.
The core argument is that standard EVT must be adapted to overcome unique actuarial data challenges, including censoring (due to limits/delays), truncation (due to maximum possible losses), and data scarcity.
Key adaptations discussed include:
Truncation and Tempering Models to account for limits or weakening tail behavior.
Censoring-Adapted Estimators (e.g., modified Hill) for incomplete data.
Splicing/Composite Models that combine body and tail distributions (e.g., Mixed Erlang/Generalized Pareto) for a full-range fit.
Advanced Regression and Multivariate Models to incorporate covariates (like climate change effects) and analyze spatial dependencies.
A profound, tailored application of EVT is deemed critical for sound pricing and risk management of catastrophic risks.

This paper introduces an 𝗶𝗻𝗻𝗼𝘃𝗮𝘁𝗶𝘃𝗲 𝗵𝘆𝗯𝗿𝗶𝗱 𝗶𝗻𝘀𝘂𝗿𝗮𝗻𝗰𝗲 𝗺𝗼𝗱𝗲𝗹 designed to cover 𝗵𝗲𝗮𝘃𝘆-𝘁𝗮𝗶𝗹𝗲𝗱 𝗹𝗼𝘀𝘀𝗲𝘀, which are extreme and potentially limitless financial damages, often associated with natural disasters. 𝗧𝗵𝗲 𝗺𝗼𝗱𝗲𝗹 𝗰𝗼𝗺𝗯𝗶𝗻𝗲𝘀 𝘁𝗿𝗮𝗱𝗶𝘁𝗶𝗼𝗻𝗮𝗹 𝗶𝗻𝗱𝗲𝗺𝗻𝗶𝘁𝘆-𝗯𝗮𝘀𝗲𝗱 𝗶𝗻𝘀𝘂𝗿𝗮𝗻𝗰𝗲 𝗳𝗼𝗿 𝘀𝗺𝗮𝗹𝗹𝗲𝗿 𝗹𝗼𝘀𝘀𝗲𝘀 𝘄𝗶𝘁𝗵 𝗽𝗮𝗿𝗮𝗺𝗲𝘁𝗿𝗶𝗰 (𝗶𝗻𝗱𝗲𝘅-𝗯𝗮𝘀𝗲𝗱) 𝗶𝗻𝘀𝘂𝗿𝗮𝗻𝗰𝗲 𝗳𝗼𝗿 𝗹𝗮𝗿𝗴𝗲𝗿, 𝗰𝗮𝘁𝗮𝘀𝘁𝗿𝗼𝗽𝗵𝗶𝗰 𝗲𝘃𝗲𝗻𝘁𝘀. A key contribution is the development of a 𝘀𝗽𝗲𝗰𝗶𝗮𝗹𝗶𝘇𝗲𝗱 𝗼𝗽𝘁𝗶𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻 𝗰𝗿𝗶𝘁𝗲𝗿𝗶𝗼𝗻 and a 𝘁𝘄𝗼-𝘀𝘁𝗲𝗽 𝗰𝗮𝗹𝗶𝗯𝗿𝗮𝘁𝗶𝗼𝗻 𝗺𝗲𝘁𝗵𝗼𝗱𝗼𝗹𝗼𝗴𝘆 that can leverage readily available covariate data, even when comprehensive loss data is scarce. Empirical analysis using both 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗲𝗱 𝗮𝗻𝗱 𝗿𝗲𝗮𝗹-𝘄𝗼𝗿𝗹𝗱 𝘁𝗼𝗿𝗻𝗮𝗱𝗼 𝗱𝗮𝘁𝗮 demonstrates that 𝘁𝗵𝗶𝘀 𝗵𝘆𝗯𝗿𝗶𝗱 𝗰𝗼𝗻𝘁𝗿𝗮𝗰𝘁 𝗼𝘂𝘁𝗽𝗲𝗿𝗳𝗼𝗿𝗺𝘀 𝘁𝗿𝗮𝗱𝗶𝘁𝗶𝗼𝗻𝗮𝗹 𝗰𝗮𝗽𝗽𝗲𝗱 𝗶𝗻𝗱𝗲𝗺𝗻𝗶𝘁𝘆 𝗰𝗼𝗻𝘁𝗿𝗮𝗰𝘁𝘀 by providing better coverage for the same premium, especially benefiting regions with limited data. The authors highlight the practical advantages of 𝗳𝗮𝘀𝘁𝗲𝗿 𝗰𝗼𝗺𝗽𝗲𝗻𝘀𝗮𝘁𝗶𝗼𝗻 and 𝗿𝗲𝗱𝘂𝗰𝗲𝗱 𝗼𝗽𝗲𝗿𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗰𝗼𝘀𝘁𝘀 offered by the parametric component.

The study explores optimal decision-making for agents minimizing risks with extremely heavy-tailed, possibly dependent losses. Focused on super-Pareto distributions, including heavy-tailed Pareto, it finds non-diversification preferred with well-defined risk measures. Equilibrium analysis in risk exchange markets indicates agents with such losses avoid risk sharing. Empirical data confirms real-world heavy-tailed distributions.