Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem

We use the Strassen theorem to solve stochastic optimization problems with stochastic dominance constraints. First, we show that a dominance-constrained problem on general probability spaces can be expressed as an infinite-dimensional optimization problem with a convenient representation of the domi...

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Vydáno v:Journal of optimization theory and applications Ročník 178; číslo 3; s. 726 - 742
Hlavní autoři: Haskell, William B., Toriello, Alejandro
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2018
Springer Nature B.V
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Dominance
Economic models
Engineering
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Probability theory
Theorems
Theory of Computation
Stochastic dominance
Strassen theorem
90C15
Convex optimization
90C25
ISSN:0022-3239, 1573-2878
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Shrnutí:We use the Strassen theorem to solve stochastic optimization problems with stochastic dominance constraints. First, we show that a dominance-constrained problem on general probability spaces can be expressed as an infinite-dimensional optimization problem with a convenient representation of the dominance constraints provided by the Strassen theorem. This result generalizes earlier work which was limited to finite probability spaces. Second, we derive optimality conditions and a duality theory to gain insight into this optimization problem. Finally, we present a computational scheme for constructing finite approximations along with a convergence rate analysis on the approximation quality.
Bibliografie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1339-9