TY - JOUR
T1 - Schur convex functionals
T2 - Fatou property and representation
AU - Grechuk, Bogdan
AU - Zabarankin, Michael
PY - 2012/4
Y1 - 2012/4
N2 - The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established onfor eitherp= 1orp=∞and with the requirement of the Fatou property, are generalized for, with no requirement of the Fatou property. In particular, the existing quantile representations for law invariant coherent risk measures and law invariant deviation measures on an atomless probability space are extended for a general probability space.
AB - The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established onfor eitherp= 1orp=∞and with the requirement of the Fatou property, are generalized for, with no requirement of the Fatou property. In particular, the existing quantile representations for law invariant coherent risk measures and law invariant deviation measures on an atomless probability space are extended for a general probability space.
KW - Deviation measures
KW - Error measures
KW - Quantile representation
KW - Risk measures
KW - Schur convexity
UR - http://www.scopus.com/inward/record.url?scp=84857014344&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84857014344&partnerID=8YFLogxK
U2 - 10.1111/j.1467-9965.2010.00464.x
DO - 10.1111/j.1467-9965.2010.00464.x
M3 - Article
AN - SCOPUS:84857014344
SN - 0960-1627
VL - 22
SP - 411
EP - 418
JO - Mathematical Finance
JF - Mathematical Finance
IS - 2
ER -