Stochastic programming with multivariate second order stochastic dominance constraints with applications in portfolio optimization

Meskarian, Rudabeh, Fliege, Jörg and Xu, Huifu (2014) Stochastic programming with multivariate second order stochastic dominance constraints with applications in portfolio optimization. Applied Mathematics & Optimization, 70 (1), 111-140. (doi:10.1007/s00245-014-9236-6).

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Abstract

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component 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 modified 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.

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e-pub ahead of print date: 11 February 2014

Published date: 1 August 2014

Keywords: multivariate stochastic dominance, second order dominance, slater constraint qualification, level function method, penalty method, portfolio optimization 90C15 90C90

Organisations: Operational Research