Tungsvansade modeller i LDA : Modellval, tröskelval och kapitalberäkning

Sammanfattning

In this study, the Loss Distribution Approach, LDA, was examined in an insurance context by modelling aggregated property-damage losses from extreme rainfall events, which are known to exhibit heavy-tailed behavior. Severity distributions were selected based on goodness-of-fit criteria, with Weibull and Gamma emerging as the most suitable for the body of the data. To capture the tail behavior more accurately, the model was complemented with the Peaks-Over-Threshold, POT, method, fitting exceedances over a threshold to a Generalized Pareto Distribution, GPD. Because closed-form expressions for the aggregate loss distribution rarely exist, Value at Risk, VaR, and Expected Shortfall, ES, were approximated numerically via Monte Carlo simulations followed by a comparison with the empirical data. A piecewise-stationarity assumption was imposed by dividing the data into decade-long blocks; KPSS tests confirmed stationarity within each block. Frequency was modeled over a 30-year window (1995–2024) to ensure adequate amounts of observations, and stationarity was likewise verified with KPSS. Independence between frequency and severity was adopted as a pragmatic simplification; future work ought to formally test it. Because the dataset lacked inflation adjustment, an index based on the Consumer Price Index, CPI, was constructed, in-flating each year’s claims in 2025 U.S. dollars. Results indicate that calibration choices and segmentation schemes strongly influence VaR and ES, underscoring the importance of systematic threshold selection methods, and the need to consider hurdle- or zero inflation models, time-varying parameters, and variance reduction techniques in Monte Carlo simulation. The findings made demonstrate that LDA, especially when combined with a GPD tail model, offers a powerful tool for actuarial capital calculations under heavy-tailed loss scenarios, though further research is required to address non-stationarity and dependency structures.