Mathematical reserve
The difference between the present value of the insurer's commitments and that of the policyholder's future premiums, the main technical liability of a life insurer.
The mathematical reserve is the liability a life insurer books for each contract. It is computed as the difference between the expected present value of what the insurer will have to pay and that of the premiums it will still receive. It exists because premiums and risk do not follow the same pattern. In a level premium death policy, the insured overpays in the early years relative to their mortality and underpays in the later ones, so the early surplus must be held, not distributed. Two assumptions drive it: the mortality table and the technical discount rate. An error in either spreads across the whole book without showing right away. Reserves must be matched by assets of at least equal amount. This covering rule forbids backing a thirty-year liability with cash. In savings type life business, the mathematical reserve is also what the policyholder would see on asking to surrender, net of any penalty.
The French Insurance Code caps the technical rate used to discount commitments at a fraction of the average government bond yield. After rates fell in the 2010s, that rule led the French market to write most of its savings contracts at a zero technical rate. The mathematical reserve there equals the accumulated savings, credited each year through profit sharing.
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