TY - JOUR
T1 - Stability and sensitivity of stochastic dominance constrained optimization models
AU - Dentcheva, Darinka
AU - Römisch, Werner
PY - 2013
Y1 - 2013
N2 - We consider convex optimization problems with kth order stochastic dominance constraints for κ ≥ 2. We discuss distances of random variables that are relevant for the dominance relation and establish quantitative stability results for optimal values and solution sets of the optimization problems in terms of a suitably selected probability metrics. Moreover, we provide conditions ensuring Hadamard directional differentiablity of the optimal value function. We introduce the notion of a shadow utility, which determines the changes of the optimal value when the underlying random variables are perturbed. Finally, we derive a limit theorem for the optimal values of empirical (Monte Carlo, sample average) approximations of dominance constrained optimization models.
AB - We consider convex optimization problems with kth order stochastic dominance constraints for κ ≥ 2. We discuss distances of random variables that are relevant for the dominance relation and establish quantitative stability results for optimal values and solution sets of the optimization problems in terms of a suitably selected probability metrics. Moreover, we provide conditions ensuring Hadamard directional differentiablity of the optimal value function. We introduce the notion of a shadow utility, which determines the changes of the optimal value when the underlying random variables are perturbed. Finally, we derive a limit theorem for the optimal values of empirical (Monte Carlo, sample average) approximations of dominance constrained optimization models.
KW - Empirical approximation
KW - Higher order stochastic dominance
KW - Risk
KW - Shadow utility
KW - Stochastic order
UR - http://www.scopus.com/inward/record.url?scp=84886302676&partnerID=8YFLogxK
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U2 - 10.1137/120886790
DO - 10.1137/120886790
M3 - Article
AN - SCOPUS:84886302676
SN - 1052-6234
VL - 23
SP - 1672
EP - 1688
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
IS - 3
ER -