TY - JOUR
T1 - Convex analysis approach to utility theories. dual utility
AU - Dentcheva, Darinka
AU - Ruszczynski, Andrzej
PY - 2012
Y1 - 2012
N2 - We show that the dual (rank dependent) utility theory and the expected utility theory have common mathematical foundations. The main results of the dual utility theory can be derived from the separation principle of convex analysis and the integral representations of continuous linear functionals. This approach is similar to the one we have successfully applied to obtain the main results of the expected utility theory. Our results explain the dual character of utility functions. Additionally, we provide two new representations of dual utility.
AB - We show that the dual (rank dependent) utility theory and the expected utility theory have common mathematical foundations. The main results of the dual utility theory can be derived from the separation principle of convex analysis and the integral representations of continuous linear functionals. This approach is similar to the one we have successfully applied to obtain the main results of the expected utility theory. Our results explain the dual character of utility functions. Additionally, we provide two new representations of dual utility.
KW - Choquet integral representation
KW - Dual utility theory
KW - Preference relations
KW - Separation
UR - http://www.scopus.com/inward/record.url?scp=84871994211&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871994211&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84871994211
SN - 1310-1331
VL - 65
SP - 1641
EP - 1648
JO - Comptes Rendus de L'Academie Bulgare des Sciences
JF - Comptes Rendus de L'Academie Bulgare des Sciences
IS - 12
ER -