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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 178; no. 3; pp. 726 - 742
Main Authors: Haskell, William B., Toriello, Alejandro
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2018
Springer Nature B.V
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1339-9