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An extreme-value theory approximation scheme in reinsurance and insurance-linked securities. (English) Zbl 1416.91151

Summary: 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, {it expected loss} and {it 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 \(L^2\) 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G10 Portfolio theory
91G20 Derivative securities (option pricing, hedging, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G70 Extreme value theory; extremal stochastic processes

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