Optimal Funding of a Liability

Funding of a given set of cash flow liabilities is typically arranged through level premium or a single premium. The question of optimality of the stream of premium payments has been largely ignored in the existing insurance literature. In this work, we propose a set of natural constraints on the premium flows and develop an optimal premium structure to fund any existing liability structure. The result shows how the least costly, yet actuarially sound, funding method—from the perspective of the insured or some more general paying agent—can be developed. The solution applies to either long-term or short-term models, but relies on deterministic assumptions, and thus is more likely to be applicable for shorter-term liabilities or those long term liabilities whose cash flows can be determined with great certainty.