Andrew Smith (UCD)

will speak on

Scale-closed two-parameter positive exponential families and mis-specification of solvency capital requirements

Time: 3:00PM
Date: Thu 3rd October 2024
Location: E0.32 (beside Pi restaurant) [map]

Abstract: Mis-specification occurs when a set of fitting probability distributions considered by a Statistician does not contain the reference distribution whence Nature generated the data. The consequences of mis-specification are particularly acute in solvency applications, where a fitted distribution is an extrapolation tool, from a small number of data points to a 1-in-200 event. By law, financial firms must hold sufficient capital to survive such events.
This talk analyses mis-specification error using a minimax approach. A Statistician and Nature each choose, independently, a scale-closed exponential family of distributions. The Statistician seeks to minimise the worst-case expected mis-specification error in capital requirements.
Our conclusion is that the Statistician should choose a fitting family in the centre of Nature's list of permitted reference families. For estimating high quantiles, Pearson's method-of-moments is more effective than maximum likelihood for mitigating mis-specification errors.

(This talk is part of the Working Group on Statistical Learning series.)

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