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By Simona Roccioletti

In this publication Simona Roccioletti experiences numerous invaluable experiences approximately hazard measures and their houses; particularly she reviews the hot (and seriously mentioned) estate of "Elicitability" of a hazard degree. extra vital, she investigates the problem concerning the backtesting of anticipated Shortfall. the most contribution of the paintings is the applying of "Test 1" and "Test 2" constructed by means of Acerbi and Szekely (2014) on assorted versions and for 5 international industry indexes.

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2. not preclude them from working at one of their fundamental business, namely trading risk. Hence, there exists a sort of trade off regulators need to assess; the basic ingredients they necessitate are: a risk measurement method, a backtesting procedure and multiplications factors (based on the outcome of the backtesting procedure). We have already evaluated the pros and cons of VaR and ES as two potential risk measurement methods, and we know that VaR is still preferred by many experts, due to its perceived superior performance in case of backtesting.

VaR and ES forecasts belong to the second group. Recently, Gneiting [25] has questioned the possibility of directly backtesting ES, as a result of the fact it is not elicitable. Undoubtedly, we can affirm that elicitability provides a natural methodology to perform backtesting. However, this does not necessarily mean that a non-elicitable functional cannot be backtested. Bellini and Bignozzi [8] state that, if we want to provide an incentive to an expected score minimizer forecaster to give an accurate assessment of a statistical functional, and if the functional at issue is elicitable, then the forecaster is induced to report a correct forecast by means of the expected score.

If a functional is elicitable, then its level sets are convex in the following sense : if F0 ∈ F, F1 ∈ F and ρ ∈ (0, 1) are such that Fρ = (1 − ρ)F0 + ρF1 ∈ F, then t ∈ T (F0 ) and t ∈ T (F1 ) imply t ∈ T (Fρ ). This result allow us to easily understand that, for example, the sum of two quantiles, not having convex level sets, is not an elicitable functional. 2 Elicitability of VaR We have pointed out that a functional is said to be elicitable, if there exists a scoring function strictly consistent for it.

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