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An Ordinal Approach to Risk Measurement


  • Marta Cardin

    () (Dept. of Applied Mathematics, University Ca'Foscari of Venice)

  • Miguel Couceiro

    () (Mathematics Research Unit, University of Luxembourg)


In this short note, we aim at a qualitative framework for modeling multivariate risk. To this extent, we consider completely distributive lattices as underlying universes, and make use of lattice functions to formalize the notion of risk measure. Several properties of risk measures are translated into this general setting, and used to provide axiomatic characterizations. Moreover, a notion of quantile of a lattice-valued random variable is proposed, which shown to retain several desirable properties of its real-valued counterpart.

Suggested Citation

  • Marta Cardin & Miguel Couceiro, 2010. "An Ordinal Approach to Risk Measurement," Working Papers 200, Department of Applied Mathematics, Universit√† Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:200

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    References listed on IDEAS

    1. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
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    3. Xu, Zeshui & Da, Qingli, 2005. "A least deviation method to obtain a priority vector of a fuzzy preference relation," European Journal of Operational Research, Elsevier, vol. 164(1), pages 206-216, July.
    4. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    5. Herrera, F. & Herrera-Viedma, E. & Chiclana, F., 2001. "Multiperson decision-making based on multiplicative preference relations," European Journal of Operational Research, Elsevier, vol. 129(2), pages 372-385, March.
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    More about this item


    lattice; risk measure; Sugeno integral; quantile.;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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