Frequency and severity
The decomposition of risk into the number of losses and the average cost per loss, the foundation of pure premium pricing.
Filip Lundberg, in his 1903 Uppsala thesis, already separated the number of claims, which he followed with a Poisson process, from the amount of each. The frequency and severity split has remained one of the first tools of actuarial work: frequency counts the claims expected over a period, severity measures the average cost of a claim when it occurs. Their product gives the expected loss, the core of the pure premium, before any loading for expenses and margin. Each component is modeled with its own distribution, Poisson or negative binomial for frequency, lognormal or Pareto for severity, and then they are combined. The split also shows where to act, prevention or business continuity. Two portfolios with the same premium can hide opposite profiles: many small claims on one side, a few very large ones on the other. Cyber combines both difficulties: frequency rising with the professionalization of attacks, and a fat-tailed severity in which extreme events dominate. Its pricing stays unstable as a result.
Textbook case: to price a cover, the actuary estimates that a company will suffer on average two incidents per year at an average cost of fifty thousand euros, giving a pure premium of one hundred thousand euros. Loadings come on top, and so does the fat tail specific to cyber.
Follow the research
One letter a week. First, the week's underwriting note, when one is published: a dated, argued decision, signed by Paul Bernardski. Then what the observatory published on cyber risk, political risk and insurance. No account, no tracking.
No spam, one-click unsubscribe, no data ever sold.