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

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  • William B. Haskell

    (National University of Singapore)

  • Alejandro Toriello

    (Georgia Institute of Technology)

Abstract

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.

Suggested Citation

  • William B. Haskell & Alejandro Toriello, 2018. "Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 726-742, September.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1339-9
    DOI: 10.1007/s10957-018-1339-9
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    References listed on IDEAS

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    1. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    2. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    3. Yu Nie & Xing Wu & Tito Homem-de-Mello, 2012. "Optimal Path Problems with Second-Order Stochastic Dominance Constraints," Networks and Spatial Economics, Springer, vol. 12(4), pages 561-587, December.
    4. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
    5. William Haskell & J. Shanthikumar & Z. Shen, 2013. "Optimization with a class of multivariate integral stochastic order constraints," Annals of Operations Research, Springer, vol. 206(1), pages 147-162, July.
    6. Radu Ioan Bot, 2010. "Conjugate Duality in Convex Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04900-2, July.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
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