An extreme-value theory approximation scheme in reinsurance and insurance-linked securities

We establish a top-down approximation scheme to approximate loss distributions of reinsurance products and Insurance-Linked Securities based on three input parameters, namely the Attachment Probability, Expected Loss and Exhaustion Probability. Our method is rigorously derived by utilizing a classical result from Extreme-Value Theory, the Pickands-Balkema-de Haan theorem. The robustness of the scheme is demonstrated by proving sharp error-bounds for the approximated curves with respect to the supremum and L² norms. The practical implications of our findings are examined by applying it to Industry Loss Warranties: the method performs very accurately for each transaction. Our approach can be used in a variety of applications such as vendor model blending, portfolio optimization and premium calculation.