Four steps

First, the tail of the loss distribution is fitted from the modelled losses using the peaks-over-threshold method of extreme value theory, with the threshold chosen by a statistical test rather than by hand; the fit returns a verdict on whether the tail is heavy enough that its average does not exist. Second, the dependence between disruption classes, the tendency of an outage, a feed failure and a regulatory action to arrive together, is modelled with a copula, a function that joins the separate loss distributions into one, so that risks recorded as independent in a register and in fact sharing a node, a vendor or a person are not summed as if separate. Third, the dollar figure is computed as the average of losses beyond a chosen quantile where that average exists, and as a bounded tail average between two quantiles where it does not, so that the headline is never a non-existent mean reported as if it had converged. Fourth, a global sensitivity analysis ranks the inputs the figure most depends on, which is also the list of where the next dollar of evidence should be spent.

Why the tail is stated

The published record of data breaches is heavy-tailed. Of four studies examined, three found tails so heavy that the mean, and in one case the variance, does not exist. A figure computed by averaging such a record is a number that does not exist, and the method does not report one.

The cap

The figure is computed under a cap that is a business fact the enterprise can name and defend: the records it holds, its policy limit and sublimits, the statutory fine ceiling, the impact tolerance it has declared to its regulator. The cap is auditable where the raw tail parameter is not, and it is the bridge between the two senses of materiality: the dollar size of the severe loss and the threshold at which the enterprise must act. For an AI estate the dependence step carries most of the figure, because a register of separate vendors resolves to a few providers, substrates and regions whose failures arrive together.

Status

The four modules each name a published method and an open-source library; none is yet wired into the product, and the bounded-tail functional is a build. The materiality figure is a forward-looking instrument and follows the reference run. The determination of materiality remains the enterprise’s.