The phenomenon whereby the historical loss distribution ceases to be representative of future losses because the underlying environment is shifting.
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 climate risk, Milly and co-authors formalized as early as 2008 in Science that stationarity was dead for hydrology, and this finding applies word for word to natural catastrophe pricing. 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.
A pricing actuary calibrates hundred-year flood frequency models on hydrological data from 1950 to 2020. The model outputs underestimate the 2021-2025 loss experience by 40 percent. The audit reveals that climate non-stationarity has shifted the distribution of extreme precipitation rightward, making the reference hundred-year event twice as frequent as it was last century.
non-stationnarité, stationnarité morte, stationarity is dead, dérive de la distribution des pertes