BeschreibungEstimating different risk measures, such as Value at Risk or Expected Shortfall, is a common task in various financial institutions. The question of evaluating and comparing these estimates is closely related to two concepts already well known in the literature: elicitability and identifiability.
A statistical functional is called elicitable if there is a strictly consistent scoring function for it, i.e. a function of two arguments, a forecast and a realization of a random variable, such that its expectation with respect to the second argument is minimized only by the correct forecast. It is called identifiable, if there is a strict identification function, i.e. again a function of two arguments such that the root of its expectation with respect to the second argument is exactly the correct forecast.
We introduce these concepts for set-valued measures of systemic risk. A banking system with n
participants is represented by a random vector Y and the quantity of interest is its aggregated outcome. The measure of systemic risk is defined as the set of n-dimensional capital allocation vectors k such that the aggregated outcome of Y+k
is acceptable under a given scalar risk measure.
We establish the link between the elicitability and/or identifiability of the systemic risk measure and the underlying scalar risk measure, taking two perspectives on the measures of systemic risk that stem from their set-valued nature.
|Zeitraum||4 Juni 2019 → 7 Juni 2019|
|Ereignistitel||SIAM Conference on Financial Mathematics & Engineering|