Pure premium

The pure premium is the fraction of the insurance premium that corresponds exactly to the mathematical expectation of claims to be indemnified, computed from frequency and severity data observed or modeled on a comparable portfolio. It represents the mathematical core of actuarial pricing: the premium the insurer would theoretically need to collect to cover its expected losses with no profit and no expenses. To move from the pure premium to the commercial premium actually charged, the actuary applies successive loadings covering acquisition costs (commissions), general management expenses, the cost of the immobilized economic capital, a security margin against volatility and, where relevant, the cost of reinsurance. The distinction between pure premium and commercial premium is fundamental in technical management: an underestimate of the pure premium inevitably produces a deteriorating loss ratio, which only becomes visible in the accounts with the lag of loss development, sometimes several years after underwriting. In cyber insurance, computing the pure premium is particularly difficult, because the rapid evolution of the threat, the correlation between exposures and the scarcity of reliable historical data make the estimation of expected claims very uncertain. Actuaries therefore resort to catastrophe models, aggregated market data and explicit prudence margins. The pure premium is also the natural denominator of the burning cost: the ratio of claims actually incurred to the exposed mass provides an empirical estimator of the past pure premium, used as the starting point for renewal.

An actuary observes, on a portfolio of 2,000 SME cyber policies, 40 claims in the year at an average cost of 80,000 euros. The frequency is 2 percent, average severity 80,000 euros: the pure premium is 2 percent times 80,000 equals 1,600 euros per policy. After loadings of 55 percent, the commercial premium is approximately 2,480 euros.

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