ACTL10001 Chap.10 Life Insurance Pricing and Reserves
Life Insurance Pricing and Reserves
Insurance pricing under the equivalence principle balances expected present values of premiums and benefits on one assumption basis. Reserving later in the contract revalues future benefits less future premiums, conditional on the policy state known at the valuation date. The distinction between immediately before and after a premium is important because that payment changes from future income to a past cashflow.
Profit emerges when mortality, investment, expenses or other experience differs from assumptions. This chapter treats premium, reserve and profit as linked but different quantities and avoids describing a reserve as merely accumulated customer premiums.
What this chapter covers
- 01
Equivalence principle
- 02
Benefit present values
- 03
Premium annuities
- 04
Net level premiums
- 05
Prospective reserves
- 06
Valuation timing
- 07
Mortality profit
- 08
Investment experience
Worked example · free
A one year net premium
- 1Benefit expected present value is 100,000 × v × 0.003.
- 1v = 1/1.04, so benefit value is $288.46.
- 1A single premium is paid at issue, so the net premium equals $288.46.
Key terms
- Equivalence Principle
- A pricing rule equating expected present values of premium and benefit cashflows under one basis.
- Net Premium
- A premium derived from benefit equivalence before commercial expense and margin additions.
- Prospective Reserve
- Expected present value of future benefits less expected present value of future premiums.
- Valuation Basis
- The mortality, interest and other assumptions used to value future cashflows.
- Mortality Profit
- A gain or loss arising when actual mortality differs from the allowance in assumptions.
- Investment Profit
- A gain or loss linked to differences between actual asset returns and assumed returns.
Life Insurance Pricing and Reserves FAQ
What does equivalence mean in pricing?
It means premium and benefit cashflows have equal expected present values under the chosen simplified basis, not that every individual policy has equal actual payments.
How does receiving a scheduled premium change a prospective reserve?
Immediately before payment the premium is still a future inflow to subtract. Immediately after receipt it is no longer future, so the reserve changes at that valuation boundary.
Is a reserve just premiums saved up?
No. A prospective reserve values remaining expected benefits less remaining expected premiums. It depends on future obligations and assumptions, not only past cash received by the insurer.
When is lower mortality favourable?
It is generally favourable for death benefit portfolios because fewer or later claims occur, but can be adverse for annuity portfolios that pay while lives survive.
Why can a future premium need a survival probability?
A later premium is usually payable only while the policyholder is alive and the contract remains in force. Its expected present value therefore combines the payment amount, discounting and the probability of reaching that premium date.
Why does reserve timing around a premium matter?
Immediately before payment, the scheduled premium is still a future inflow and is subtracted in a prospective reserve. Immediately after payment, that inflow has occurred and disappears from the future premium value. The remaining benefit promise may be almost unchanged, so the reserve can differ by roughly the premium at that boundary.
Always attach the timing label to a reported reserve rather than leaving the valuation instant implicit. Use the same mortality and interest basis on both sides.
Exam move
Begin every pricing exercise by drawing benefit and premium streams separately. Apply survival or death probabilities to both, because later premiums may also be contingent on survival. For reserves, cross out past cashflows and state whether valuation is before or after a scheduled payment. Practise explaining mortality and investment deviations by product type rather than memorising universal favourable directions.
Finish with the limits of the net model, including omitted expenses, capital and margins. Separate the contract into premium branches and benefit branches before applying the equivalence principle. Mark which premiums are certain at issue and which require survival to a later date. For each benefit, specify the death or survival event and settlement time so its probability and discount exponent are paired correctly.
Sum the expected present values on each side and solve only after the full branch structure is visible. Test the premium by substituting it back into the original equivalence equation. For reserves, draw a vertical valuation line through the cashflow diagram and remove everything already paid. State whether the line falls immediately before or after a premium, since that choice changes future inflows.
Calculate a prospective reserve from remaining benefits less remaining premiums and interpret the sign from the insurer's viewpoint. Create sensitivity drills that alter interest or mortality while holding other assumptions fixed, then explain why the effect depends on product cashflows. Distinguish experience profit over a period from a reserve at a date.
A favourable mortality deviation for death cover may have a different direction from the same survival experience on an annuity portfolio. Keep the stated basis attached to every value and note that net models omit expenses, margins, lapses and capital. End by describing the result as a valuation under assumptions, not a guaranteed policy account balance.
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