Prospective Policy Value¶

Definition¶

The prospective gross policy value at duration $t$ is $V_t=\mathbb{E}[L_t^g\mid\text{policy in force at }t]$ $policy in force at t]$ . Equivalently, it is the expected time- $t$ present value (PV) of future benefits and expenses minus the expected time- $t$ PV of future premiums, under the selected valuation basis and timing convention, provided the in-force event has positive probability and the future loss is integrable.

Interpretation¶

The value measures the expected remaining liability of an active policy. It changes as the insured ages and as benefits and premium payments approach or pass.

Timeline split at duration t: grey premiums before t are ignored, while future premiums with expectation 30 and future benefits and expenses with expectation 50 give V_t = 20.

The figure looks forward from duration $t$ with the numbers from the Examples. Premiums already paid (grey) play no part; given that the policy is in force, future premiums have expected value 30 at time $t$ and future benefits and expenses 50, so $V_t=50-30=20$ $20$ . The arrows are schematic: the figure fixes only the two expected totals, not individual cash flows.

The future loss random variable supplies $L_t^g=Z_t+H_t-Y_t$ $Y_{t}$ . Conditional expectation given an event describes averaging after information is fixed; here the information is that the policy remains in force at $t$ . Averaging the remaining net outgo under that condition gives the policy value.

Key Results¶

$V_t+\mathbb{E}[Y_t\mid\text{in force}]=\mathbb{E}[Z_t+H_t\mid\text{in force}]$ $in force]$ .
Net policy values omit expenses and use the corresponding net premium.
A value at issue is zero under matching equivalence assumptions; this need not hold at later durations or after a change of basis.
An expected-liability value is not, by itself, a complete capital requirement for adverse outcomes.

Examples¶

If expected remaining benefits and expenses are 50 and expected remaining premiums are 30, the prospective policy value is 20 at the specified valuation time.

Prerequisites¶

Sources¶

Life Insurance · Lecture 7

Aliases: prospective reserve, gross premium policy value, policy value, policy reserve, net premium policy value, benefit reserve, mathematical reserve Keywords: t V, E[L t | in force], expected future outgo minus income, zero at issue under the equivalence principle

Last updated: 17 October 2026 21:53