Appl Math Optim (2014) 70:111–140
Stochastic Programming with Multivariate Second
Order Stochastic Dominance Constraints with
Applications in Portfolio Optimization
Rudabeh Meskarian · Jörg Fliege · Huifu Xu
Published online: 11 February 2014
© Springer Science+Business Media New York 2014
Abstract In this paper we study optimization problems with multivariate stochas-
tic dominance constraints where the underlying functions are not necessarily linear.
These problems are important in multicriterion decision making, since each compo-
nent of vectors can be interpreted as the uncertain outcome of a given criterion. We
propose a penalization scheme for the multivariate second order stochastic dominance
constraints. We solve the penalized problem by the level function methods, and a mod-
iﬁed cutting plane method and compare them to the cutting surface method proposed
in the literature. The proposed numerical schemes are applied to a generic budget
allocation problem and a real world portfolio optimization problem.
Keywords Multivariate stochastic dominance · Second order dominance ·
Slater constraint qualiﬁcation · Level function method · Penalty method ·
Mathematics Subject Classiﬁcation 90C15 · 90C90
Communicated by J. F. Bonnans.
R. Meskarian (
Department of Engineering Systems and Design, Singapore University of Technology and Design,
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK
School of Engineering and Mathematical Sciences, City University London, London EC1V 0HB, UK