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Beyond Markowitz with multiple criteria decision aiding

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Abstract

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.

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Acknowledgements

The third author wishes to acknowledge financial support from the Polish National Science Centre, grant no. NN519 441939.

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Authors and Affiliations

  1. Department of Economics and Business, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo

  2. Institute of Computing Science, Poznań University of Technology, ul. Piotrowo 2, 60-965, Poznan, Poland

    Roman Słowiński

  3. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Roman Słowiński

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  1. Salvatore Greco
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  2. Benedetto Matarazzo
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  3. Roman Słowiński
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Correspondence to Salvatore Greco.

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Greco, S., Matarazzo, B. & Słowiński, R. Beyond Markowitz with multiple criteria decision aiding. J Bus Econ 83, 29–60 (2013). https://doi.org/10.1007/s11573-012-0644-2

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