Actuarial & Insurance

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Loss Reserve

Money set aside for claims incurred but not yet fully paid.

Formula

R = \hat{C} - C_{paid}

Variables

RReserve

ĈEstimated ultimate claims

C_{paid}Claims paid so far

Example

Ultimate $12M, paid $8M: R = $4M

Did You Know?

Under-reserving has sunk many insurers — estimating future claims is one of the actuary's hardest jobs.

actuarial reserve claims

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Pure Premium

Expected claim cost per policy: frequency times severity.

Gross Premium

Premium that covers claims plus an expense/profit load.

Loss Ratio

Claims paid divided by premiums earned.

Combined Ratio

Total cost ratio: losses plus expenses vs premium.

Expected Value of a Claim

Probability-weighted average of possible claim amounts.

Present Value of an Annuity

Value today of a stream of future payments.