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Stochastically weighted stochastic dominance concepts with an application in capital budgeting

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  • Hu, Jian
  • Homem-de-Mello, Tito
  • Mehrotra, Sanjay

Abstract

The problem of comparing random vectors arises in many applications. We propose three new concepts of stochastically weighted dominance for comparing random vectors X and Y. The main idea is to use a random vector V to scalarize X and Y as VTX and VTY, and subsequently use available concepts from stochastic dominance and stochastic optimization for comparison. For the case where the distributions of X, Y and V have finite support, we give (mixed-integer) linear inequalities that can be used for random vector comparison as well as for modeling of optimization problems where one of the random vectors depends on decisions to be optimized. Some advantages of the proposed new concepts are illustrated with the help of a capital budgeting example.

Suggested Citation

  • Hu, Jian & Homem-de-Mello, Tito & Mehrotra, Sanjay, 2014. "Stochastically weighted stochastic dominance concepts with an application in capital budgeting," European Journal of Operational Research, Elsevier, vol. 232(3), pages 572-583.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:3:p:572-583
    DOI: 10.1016/j.ejor.2013.08.007
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    References listed on IDEAS

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    1. Jian Hu & Tito Homem-de-Mello & Sanjay Mehrotra, 2011. "Risk-adjusted budget allocation models with application in homeland security," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 819-839.
    2. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, University Library of Munich, Germany.
    3. 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.
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    Cited by:

    1. Leilei Zhang & Tito Homem-de-Mello, 2017. "An Optimal Path Model for the Risk-Averse Traveler," Transportation Science, INFORMS, vol. 51(2), pages 518-535, May.
    2. Post, Thierry, 2016. "Standard Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1009-1020.
    3. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    4. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.

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