TY - JOUR
T1 - Risk preferences on the space of quantile functions
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
N1 - Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.
PY - 2013/12
Y1 - 2013/12
N2 - We propose a novel approach to quantification of risk preferences on the space of nondecreasing functions. When applied to law invariant risk preferences among random variables, it compares their quantile functions. The axioms on quantile functions impose relations among comonotonic random variables. We infer the existence of a numerical representation of the preference relation in the form of a quantile-based measure of risk. Using conjugate duality theory by pairing the Banach space of bounded functions with the space of finitely additive measures on a suitable algebra Σ, we develop a variational representation of the quantile-based measures of risk. Furthermore, we introduce a notion of risk aversion based on quantile functions, which enables us to derive an analogue of Kusuoka representation of coherent law-invariant measures of risk.
AB - We propose a novel approach to quantification of risk preferences on the space of nondecreasing functions. When applied to law invariant risk preferences among random variables, it compares their quantile functions. The axioms on quantile functions impose relations among comonotonic random variables. We infer the existence of a numerical representation of the preference relation in the form of a quantile-based measure of risk. Using conjugate duality theory by pairing the Banach space of bounded functions with the space of finitely additive measures on a suitable algebra Σ, we develop a variational representation of the quantile-based measures of risk. Furthermore, we introduce a notion of risk aversion based on quantile functions, which enables us to derive an analogue of Kusuoka representation of coherent law-invariant measures of risk.
KW - Conjugate duality
KW - Kusuoka representation
KW - Quantile functions
KW - Risk measures
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U2 - 10.1007/s10107-013-0724-2
DO - 10.1007/s10107-013-0724-2
M3 - Article
AN - SCOPUS:84920257788
SN - 0025-5610
VL - 148
SP - 181
EP - 200
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1-2
ER -