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

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