prospective vs retrospective reserves

There are two natural ways to figure out how much money a policy should have accumulated by now. You can look FORWARD and ask 'how much do I still owe in future benefits, beyond the premiums I'll still collect?' Or you can look BACKWARD and ask 'how much have I taken in so far, grown with interest, minus what I've already paid out in claims?' These are the prospective and retrospective reserves — the same reserve seen from the future versus the past.

Precisely, the prospective reserve equals the present value of future benefits minus the present value of future net premiums (a forward-looking obligation). The retrospective reserve equals the accumulated value of past net premiums minus the accumulated cost of past benefits, all rolled forward at interest and adjusted for the survivors who remain (the accumulated past contributions of this cohort, per survivor). A foundational theorem says that — provided both calculations use exactly the same mortality, interest, and premium basis, and the premium was set by the equivalence principle — the two give an identical answer at every duration.

The equivalence is more than a curiosity. It gives actuaries two independent routes to the same number, which is a powerful error-check, and it lets you choose whichever is easier for a given product (prospective is usually simpler for benefits known in the future; retrospective is handy when premiums and past experience are easy to accumulate). The catch: the two stop matching the moment you change the basis partway — for example reserving on a different interest rate than pricing — so equivalence is a property of a consistent basis, not a law of nature.