BeschreibungWe establish elicitability and identifiability results for measures of systemic risk introduced in Feinstein, Rudloffand Weber (SIAM J. Financial Math. 2017). These risk measures determine the set of all capital allocations that make a financial system acceptable. Hence, they take an ex ante angle, specifying those capital allocations that prevent the system from default. At the same time, they allow to capture the dependence structure of different financial firms. The elicitability of a risk measure, or more generally, a statistical functional, amounts to the existence of a strictly consistent scoring or loss function. That is a function in two arguments, a forecast and an observation, such that the expected score is minimised by the correctly specified functional value, thereby encouraging truthful forecasts. Prominent examples are the squared loss for the mean and the absolute loss for the median. Hence, the elicitability of a functional is crucial for meaningful forecast comparison and forecast ranking, but also opens the way to M-estimation and regression.To allow for a rigorous treatment of elicitability of set-valued functionals, we introduce two modes of elicitability: a selective and an exhaustive version. We show that these two modes are mutually exclusive and establish exhaustive elicitability results for the systemic risk measures under consideration. That means we construct strictly consistent scoring functions taking sets as input arguments for forecasts.Our construction relies on a mixture representation of elementary scores akin to the one established for quantiles and expectiles in Ehm, Gneiting, Jordan and Krüger (JRSS B, 2016). This naturally leads to multivariate Murphy diagrams which can become an important diagnostic tool in evaluating forecasts simultaneously with respect to all consistent scoring functions.
|Zeitraum||22 Juli 2019 → 26 Juli 2019|
|Ereignistitel||European Meeting of Statisticians|