Economic Neutral Position: How to best replicate not fully replicable liabilities

Andreas Kunz and Markus Popp

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Abstract: Financial undertakings often have to deal with liabilities of the form 'non-hedgeable claim size times value of a tradeable asset', e.g. foreign property insurance claims times fx rates. Which strategy to invest in the tradeable asset is risk minimal? We generalize the Gram-Charlier series for the sum of two dependent random variable, which allows us to expand the capital requirements based on value-at-risk and expected shortfall. We derive a stable and fairly model independent approximation of the risk minimal asset allocation in terms of the claim size distribution and the moments of asset return. The results enable a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component.

Date: 2017-04, Revised 2019-07
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Published in Insurance Mathematics and Economics, 2012, Vol 96, 53-67

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