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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. 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.
    2. Radu Ioan Bot, 2010. "Conjugate Duality in Convex Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04900-2, October.
    3. 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.
    4. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    5. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    6. 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.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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