Actuarial & Insurance

Basic

Expected Value of a Claim

Probability-weighted average of possible claim amounts.

Formula

E[X] = \sum p_i x_i

Variables

E[X]Expected claim

p_iProbability of outcome i

x_iClaim amount i

Example

1% chance of $50,000: E[X] = $500

Did You Know?

Insurance works by pooling many small, predictable expected values against rare, ruinous individual losses.

actuarial expected value risk

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More in Actuarial & Insurance

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.

Present Value of an Annuity

Value today of a stream of future payments.

Future Value of an Annuity

Accumulated value of regular contributions.