Actuarial non-stationarity

In February 2008, Milly and co-authors ran the headline "Stationarity Is Dead" in Science: for hydrology, the past no longer describes the law of future floods, and the finding applies word for word to natural catastrophe pricing. Stationarity is the implicit founding hypothesis of all actuarial pricing: the probability distribution of losses observed in the past remains representative of the one that will generate future losses. As long as this holds, computing a pure premium reduces to estimating the mean and variance of a stable distribution. Non-stationarity describes the case where this condition no longer holds, either because exposure changes, or because loss frequency or severity drifts under the effect of a structural external factor. In cyber risk, non-stationarity is even more pronounced: attack techniques, the topology of exploited vulnerabilities and the structure of target networks evolve faster than actuaries can build representative historical series. In both cases the effect is identical: a premium calibrated on history structurally underestimates future loss experience, and reserves built on that basis prove insufficient. Actuarial responses to non-stationarity include prospective scenario modeling, real-time-recalibrated catastrophe models, and revision of the data windows retained for calibration.