TY - JOUR
T1 - Optimization with multivariate stochastic dominance constraints
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
PY - 2009/3
Y1 - 2009/3
N2 - We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann-Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions.
AB - We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann-Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions.
KW - Duality
KW - Optimality
KW - Risk
KW - Stochastic order
KW - Utility
UR - http://www.scopus.com/inward/record.url?scp=46749102111&partnerID=8YFLogxK
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U2 - 10.1007/s10107-007-0165-x
DO - 10.1007/s10107-007-0165-x
M3 - Article
AN - SCOPUS:46749102111
SN - 0025-5610
VL - 117
SP - 111
EP - 127
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1-2
ER -