Actuarial & Insurance
Intermediate

Gross Premium

Premium that covers claims plus an expense/profit load.

Formula

GP=PP1−eGP = \frac{PP}{1 - e}

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Variables

GPGross premium
PPPure premium
eExpense ratio

Example

PP=$400, e=0.3: GP ≈ $571

Did You Know?

The expense ratio bundles commissions, admin and profit into the premium you actually pay.

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Pure Premium

Intermediate

Expected claim cost per policy: frequency times severity.

Loss Ratio

Basic

Claims paid divided by premiums earned.

Combined Ratio

Intermediate

Total cost ratio: losses plus expenses vs premium.

Expected Value of a Claim

Basic

Probability-weighted average of possible claim amounts.

Present Value of an Annuity

Intermediate

Value today of a stream of future payments.

Future Value of an Annuity

Intermediate

Accumulated value of regular contributions.