This thesis reviewed various heavy tailed distributions and Extreme Value Theory (EVT) to estimate the catastrophic losses simulated from Florida Public Hurricane Loss Projection Model (FPHLPM). We have compared risk measures such as Probable Maximum Loss (PML) and Tail Value at Risk (TVaR) of the selected distributions with empirical estimation to capture the characteristics of the loss data as well as its tail distribution. Generalized Pareto Distribution (GPD) is the main focus for modeling the tail losses in this application. We found that the hurricane loss data generated from FPHLPM were consistent with historical losses and were not as heavy as expected. The tail of the stochastic annual maximum losses can be explained by an exponential distribution. This thesis also touched on the philosophical implication of small probability, high impact events such as Black Swan and discussed the limitations of quantifying catastrophic losses for future inference using statistical methods.

This thesis introduces various approaches to natural catastrophe risk assessment in (re)insurance environment. Most emphasis and further elaboration is put on probabilistic models in comparison to the standard model as proposed by Solvency II. The outcomes of natural catastrophe modeling play an important role in the design of proper actuarial models related to catastrophe risk. More specifically it is shown that they can be entirely understood in a wider actuarial context, namely risk theory. Within the Solvency II framework, probabilistic model outcomes are translated by means of the proposed decomposition methodology putting them into a similar language of the standard formula in order to create the ability to compare different results implied by either probabilistic model or standard formula. This enables both comparison of the implied dependence structure of probabilistic model to standardized correlations assumed in Solvency II, and scenario year loss factors of Solvency II to implied damage factors of probabilistic models in defined cresta zones. The introduced decomposition methodology is illustrated by flood and windstorm model outcomes calculated on exposure data of Czech insurance companies and compared to the respective standard formula parameters and outcomes. Finally, other applications of the proposed decomposition methodology are introduced, such as measurement of diversification effect or blending of different results calculated by different models or even approaches to natural catastrophe risk assessment.