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**Fissler, Tobias.** 2018. Elicitability and Identifiability of Measures of Systemic Risk. 6th Imperial-ETH Workshop on Mathematical Finance, Zürich, Schweiz, 04.04.-06.04.

BibTeX

## Abstract

We establish elicitability and identifiability results for systemic risk measures of the form R(Y)={k∈Rn|ρ(Λ(Y+k))≤0}. Here, Λ:Rn→R is an increasing aggregation function, ρ is a real-valued risk measure, and the random vector Y represents a system of n financial firms. That means the risk measure R(Y) takes an a priori perspective, being the set of all capital allocation k∈Rn which make the aggregated system Λ(Y+k) acceptable under ρ. 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. An identification function is similar to a scoring function, however, the correctly specified forecast is the zero of the expected identification function rather than its minimizer, thus giving rise to Z-estimation and possibilities to assess the calibration of forecasts.In this talk, we show the intimate link between the elicitability / identifiability of ρ and R making use of an integral construction. On the one hand, our results appear to be relevant and beneficial from an applied point of view. On the other hand, they turn out to be the first (non-trivial) results on set-valued functionals in the theory of elicitability, thereby establishing a novelty of theoretical interest on its own.

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## Publication's profile

Status of publication | Published |
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Affiliation | External |

Type of publication | Paper presented at an academic conference or symposium |

Language | English |

Title | Elicitability and Identifiability of Measures of Systemic Risk |

Event | 6th Imperial-ETH Workshop on Mathematical Finance |

Year | 2018 |

Date | 04.04.-06.04. |

Country | Switzerland |

Location | Zürich |

URL | https://math.ethz.ch/imsf/events/conferences-and-workshops/past-events/2018/imperial-eth-2018.html |