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, computed as the difference between the expected present value of what it will have to pay and the expected present value of the premiums it will still receive. Its necessity comes from the mismatch between the pattern of premiums and the pattern of risk: in a level premium death policy the insured overpays in the early years relative to their mortality and underpays in the later ones, and the early surplus must be held, not distributed. Two assumptions drive it, the mortality table and the technical discount rate, and an error in either propagates across the whole book without showing immediately. Reserves must be matched by assets of at least equal amount, a covering rule that 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, a rule that led the French market to write most of its savings contracts at a zero technical rate after the interest rate decline of the 2010s. The mathematical reserve there equals the accumulated savings, credited each year through profit sharing.
provision technique vie, réserve mathématique