TY - JOUR
T1 - Robust stochastic dominance and its application to risk-averse optimization
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
PY - 2010/5
Y1 - 2010/5
N2 - We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconvex case, we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem.
AB - We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconvex case, we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem.
KW - Risk constraints
KW - Robust preferences
KW - Semi-infinite optimization
KW - Stochastic dominance constraints
KW - Stochastic order
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U2 - 10.1007/s10107-009-0321-6
DO - 10.1007/s10107-009-0321-6
M3 - Article
AN - SCOPUS:73549107865
SN - 0025-5610
VL - 123
SP - 85
EP - 100
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1
ER -