2014-04-04Buch DOI: 10.18452/3064
Multi-Objective Probabilistically Constrained Programming with Variable Risk: New Models and Applications
Lejeune, Miguel A.
We consider a class of multi-objective probabilistically constrained problems MOPCP with a joint chance constraint, a multi-row random technology matrix, and a risk parameter (i.e., the reliability level) defined as a decision variable. We propose a Boolean modeling framework and derive a series of new equivalent mixed-integer programming formulations. We demonstrate the computational efficiency of the formulations that contain a small number of binary variables. We provide modeling insights pertaining to the most suitable reformulation, to the trade-off between the conflicting cost/revenue and reliability objectives, and to the scalarization parameter determining the relative importance of the objectives. Finally, we propose several MOPCP variants of multi-portfolio financial optimization models that implement a downside risk measure and can be used in a centralized or decentralized investment context. We study the impact of the model parameters on the portfolios, show, via a cross-validation study, the robustness of the proposed models, and perform a comparative analysis of the optimal investment decisions.
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