Optimization with Stochastic Dominance Constraints

By Darinka Dentcheva †, Andrzej Ruszczynski. SIAM Journal on Optimization, 2003

407 citations recorded by the source corpus.

We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/324426070c0032e4f1e9a04b634dd50700760d4d

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Citations in the corpus

Portfolio optimization with stochastic dominance constraints (2006, background): “JEL classification: C44; C61; G11 Keywords: Portfolio optimization; Stochastic dominance; Stochastic order; Risk; Utility function; Duality”
Optimal Path Problems with Second-Order Stochastic Dominance Constraints (2012, methodology): “Interestingly, when SSD is concerned, the dominance relationship can be represented with a finite number of linear constraints, which leads to the recently-introduced optimization problems with stochastic dominance constraints (OP-SD) (Dentcheva & Ruszczynski 2003, Dentcheva & Ruszczynski 2004).”
Lectures on Stochastic Programming: Modeling and Theory (2009, methodology): “Models with stochastic dominance constraints are introduced and analyzed by Dentcheva and Ruszczyński in [62, 64, 65].”
Higher moment coherent risk measures (2007, unknown): “programming, see Prékopa (1995)), reliability theory, etc.”
Modeling Heterogeneous Risk-Taking Behavior in Route Choice: A Stochastic Dominance Approach (2011, background): “See Dentcheva and Ruszczynski (2003). h Given two paths krs and lrs, it follows from the lemma that prsk 2prsl !”
Semi-infinite probabilistic optimization: first-order stochastic dominance constrain (2004, unknown): “Define for a given random variable Y 2 L1ð ,F ,PÞ two sets Að1ÞðYÞ 1⁄4 fX 2 L1ð ,F ,PÞ : X ð1ÞYg, Að2ÞðYÞ 1⁄4 fX 2 L1ð ,F ,PÞ : X ð2ÞYg: The set Að2ÞðYÞ is convex and closed in L1ð ,F ,PÞ, as proved in [8].”
Portfolio selection models: a review and new directions (2009, methodology): “Several authors proposed formulations and solution methods for such models ([7], [8], [42], [10]).”
Monte Carlo sampling-based methods for stochastic optimization (2014, methodology): “This issue is circumvented when the random variable Y has finitely many outcomes y 1 , . . . , y r ; in that case, Dentcheva and Ruszczy´nski [58] show that it suffices to write the constraints in (47) only for η = y j , j = 1, . . . , r, thus yielding a problem with finitely many expected-value con”
An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011, methodology): “In their SSD-constrained model (1), Dentcheva and Ruszczyński characterize stochastic dominance with criterion (b) of section 1.1. They prove that if b R has a discrete finite distribution with realizations br ð1Þ, . . . ,br ðS Þ, then Rx SSD b R is equivalent to a finite system of inequalities Eð1⁄”