Pure premium

Category: Actuarial fundamentals · Reviewed by Chrissie Anderson, Client Executive · Last reviewed

Pure premium

The pure premium is the expected loss cost per exposure unit, ignoring any loading for expenses, profit, contingencies or capital cost. It is the unconditional expected value of claim payments that the insurer must make in respect of the risk.

Components

Pure premium = expected frequency × expected severity

Or, for a more sophisticated decomposition:

Pure premium = E[N] × E[X | N ≥ 1]

where N is the number of claims and X is the severity per claim. For aggregate losses on a portfolio, the collective risk model (Tweedie, compound Poisson, etc.) is typically used.

Position in the premium build-up

In a typical commercial rating sheet:

1. Pure premium (expected loss).
2. Risk premium = pure premium + loading for parameter uncertainty / volatility.
3. Office premium = risk premium + expenses + commission + profit.
4. Gross premium = office premium + Insurance Premium Tax + levies.

Terminology variation

US actuarial literature often uses “pure premium” interchangeably with “loss cost”. UK and European literature treats them as broadly synonymous in general insurance contexts.

References

• IFoA. Practical Guide to GI Pricing.
• CAS (2010). Foundations of Casualty Actuarial Science.

Cross-references

• Risk premium
• Office premium
• Burning cost
• Loss cost

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Maintained by Matt Bartlett, Director, Apex Insurance Brokers Limited. FCA FRN 724952. Companies House 07014570.