"We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing condition. This enables an insurance market to be established even if the two funds face the same mortality risk, so long as they have different risk preferences. Provided the preferences of the two funds are not too dissimilar, insurance provides little benefit, implying the base scheme is effectively optimal. When preferences vary significantly, insurance can be beneficial."
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