Actuarial & Insurance

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Risk Premium (Variance Load)

Premium that adds a load proportional to risk variance.

Formula

P = E[X] + \theta\,\text{Var}(X)

Variables

PPremium

E[X]Expected loss

θRisk-aversion factor

Var(X)Variance of loss

Example

Riskier, more volatile lines carry a bigger variance load.

Did You Know?

Insurers charge extra for volatile risks because a rare huge claim threatens solvency more than steady losses.

actuarial risk premium

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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.