Pure premium

The pure premium, also called risk premium or loss cost, is the part of the premium that pays for expected claims and nothing else, the expected value of losses. It is frequency × average severity, both observed or modeled on a comparable book; US ratemaking writes the same thing as losses divided by exposure units. Every actuarial rate starts there, since it is what the insurer would need to collect to pay its expected losses, with no expenses and no profit. To get to the gross premium the insured actually pays, the actuary adds loadings: acquisition costs (commissions), administrative expenses, the cost of the capital tied up, a margin for volatility and, where relevant, the cost of reinsurance. The two get mixed up all the time. Pure premium is an expected cost, gross premium is a price. An underestimated pure premium always ends in a worse loss ratio, but the accounts only show it as claims develop, sometimes years after the business was written. In cyber the exercise is hard. The threat changes fast, exposures are correlated and reliable history is thin, so actuaries lean on catastrophe models, pooled market data and explicit prudence margins. Burning cost gives an empirical read, since past claims divided by insured exposure estimate the past pure premium, which is where a renewal starts.