Operational Research

, Volume 19, Issue 3, pp 661–677 | Cite as

Characterizing compromise solutions for investors with uncertain risk preferences

  • Francisco Salas-MolinaEmail author
  • Juan A. Rodríguez-Aguilar
  • David Pla-Santamaria
Original Paper


The optimum portfolio selection for an investor with particular preferences was proven to lie on the normalized efficient frontier between two bounds defined by the Ballestero (J Oper Res Soc 49:998–1000, 1998) bounding theorem. A deeper understanding is possible if the decision-maker is provided with visual and quantitative techniques. Here, we derive useful insights as a way to support investor’s decision-making through: (1) a new theorem to assess balance of solutions; (2) a procedure and a new plot to deal with discrete efficient frontiers and uncertain risk preferences; and (3) two quality metrics useful to predict long-run performance of investors.


Finance Portfolio selection Compromise programming Discrete efficient-frontiers Performance prediction 

Mathematics Subject Classification




Work partially funded by projects Collectiveware TIN2015-66863-C2-1-R (MINECO/FEDER) and 2014 SGR 118.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Hilaturas Ferre, S.A.Banyeres de MariolaSpain
  2. 2.IIIA-CSICCerdanyolaSpain
  3. 3.Escuela Politécnica Superior de AlcoyAlcoySpain

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