Actuarial & Insurance
Intermediate

Pure Premium

Expected claim cost per policy: frequency times severity.

Formula

PP=f×SPP = f \times S

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Variables

PPPure premium
fClaim frequency
SAverage claim severity

Example

f=0.05, S=$8000: PP = $400

How it works

Pure premium is the average amount an insurer expects to pay in claims for one policy before adding expenses, profit, and risk margins. It works because total expected claim cost can be broken into two parts: how often a claim happens (frequency) and how much the average claim costs when it does happen (severity), so multiplying them gives the expected cost per policy.

When to use it

Use this when pricing insurance, analyzing loss experience, or estimating expected claim costs from historical data. It is especially useful in ratemaking, where you need a base claim cost before loading for admin costs, commissions, and profit.

Worked example, step by step

Suppose an insurer expects 0.12 claims per policy per year and the average claim payment is $3,500. PP = f × S PP = 0.12 × 3500 PP = 420 Pure premium = $420 per policy per year

Common mistakes to avoid

  • Using total claims paid instead of average claim severity
  • Confusing frequency as a percentage without converting it to a decimal
  • Treating pure premium as the final insurance price instead of just the expected claim cost

Did You Know?

The pure premium is the bare cost of risk — insurers add loadings for expenses and profit on top.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026