TY - UNPB

T1 - Disentangling distortion risk measures and the Expected Shortfall

AU - Amarante, Massimiliano

AU - Liebrich, Felix-Benedikt

PY - 2022/7/20

Y1 - 2022/7/20

N2 - Distortion risk measures are risk measures that are law invariant and comonotonic addi- tive. We characterize notable sub-classes of this wide range of functionals, starting with the property of prudence recently introduced by Wang & Zitikis. Moreover, we develop a new view of coherent distortion risk measures and show that they are captured by a single probability charge. By linking our insights into these two properties, we obtain new characterizations of the Expected Shortfall and implications associated with its utilization as standard measure of market risk. Along the route, we obtain some ancillary results of independent interest. These concern: (i) the anticore of a general submodular distortion; (ii) a full characterization of spectral risk measures on integrable random variables; and (iii) a novel proof of the automatic Fatou property of convex, law invariant risk measures. Finally, we fully close the remaining gap to the Wang-Zitikis axiomatization of the Expected Shortfall and carefully disentangle the interplay of the involved axioms within the large class of distortion risk measures.

AB - Distortion risk measures are risk measures that are law invariant and comonotonic addi- tive. We characterize notable sub-classes of this wide range of functionals, starting with the property of prudence recently introduced by Wang & Zitikis. Moreover, we develop a new view of coherent distortion risk measures and show that they are captured by a single probability charge. By linking our insights into these two properties, we obtain new characterizations of the Expected Shortfall and implications associated with its utilization as standard measure of market risk. Along the route, we obtain some ancillary results of independent interest. These concern: (i) the anticore of a general submodular distortion; (ii) a full characterization of spectral risk measures on integrable random variables; and (iii) a novel proof of the automatic Fatou property of convex, law invariant risk measures. Finally, we fully close the remaining gap to the Wang-Zitikis axiomatization of the Expected Shortfall and carefully disentangle the interplay of the involved axioms within the large class of distortion risk measures.

M3 - Working paper/Discussion paper

BT - Disentangling distortion risk measures and the Expected Shortfall

ER -