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Multi-objective probabilistically constrained programs with variable risk: Models for multi-portfolio financial optimization

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  • Lejeune, Miguel A.
  • Shen, Siqian

Abstract

We consider a class of multi-objective probabilistically constrained programs (MOPCP) with a joint probabilistic constraint and a variable risk level. We consider two cases with only a random right-hand side vector or a multi-row random technology matrix, and propose a Boolean modeling framework to derive new mixed-integer linear programs (MILP) that are either equivalent reformulations or inner approximations of MOPCP, respectively. Via testing randomly generated MOPCP instances, we demonstrate modeling insights pertaining to the most suitable MILP, to the trade-offs between conflicting objectives of cost/revenue and reliability, and to the parameter scalarization determining relative importance of each objective. We then focus on several MOPCP variants of a multi-portfolio financial optimization problem to implement a downside risk measure, which can be used in a centralized or decentralized investment context. We study the impact of modeling parameters on the portfolios, show, via a cross-validation study, robustness of MOPCP, and perform a comparative analysis of the optimal investment decisions.

Suggested Citation

  • Lejeune, Miguel A. & Shen, Siqian, 2016. "Multi-objective probabilistically constrained programs with variable risk: Models for multi-portfolio financial optimization," European Journal of Operational Research, Elsevier, vol. 252(2), pages 522-539.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:2:p:522-539
    DOI: 10.1016/j.ejor.2016.01.039
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    8. Yiling Zhang & Jin Dong, 2022. "Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1531-1547, May.
    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2017. "Differential equations connecting VaR and CVaR," INDEM - Working Paper Business Economic Series 24017, Instituto para el Desarrollo Empresarial (INDEM).

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