TY - JOUR
T1 - Common mathematical foundations of expected utility and dual utility theories
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
PY - 2013
Y1 - 2013
N2 - We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models.
AB - We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models.
KW - Choquet representation
KW - Preferences
KW - Rank-dependent utility functions
KW - Separation
KW - Utility functions
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U2 - 10.1137/120868311
DO - 10.1137/120868311
M3 - Article
AN - SCOPUS:84877782679
SN - 1052-6234
VL - 23
SP - 381
EP - 405
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 1
ER -