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AN EXTREME-VALUE THEORY APPROXIMATION SCHEME IN REINSURANCE AND INSURANCE-LINKED SECURITIES

Part of: Mathematical economics

Published online by Cambridge University Press:  03 July 2018

Rom Aviv
Rom Aviv*
Affiliation:
IBI ILS Partners LTD., Shalom Tower, 9 Ahad Ha'Am St, 28th floor, Tel-Aviv 6129101, Israel E-Mail: [email protected]
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Abstract

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.

Keywords

Extreme-value theoryloss exceedance probability curvereinsuranceinsurance-linked securities

MSC classification

Primary: 91B50: General equilibrium theory
Secondary: 91B16: Utility theory
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1157 - 1173
Copyright
Copyright © Astin Bulletin 2018 

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