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Conditional Submodular Coherent Risk Measures

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 854))

Abstract

A family of conditional risk measures is introduced by considering a single period financial market, relying on a notion of conditioning for submodular capacities, which generalizes that introduced by Dempster. The resulting measures are expressed as discounted conditional Choquet expected values, take into account ambiguity towards uncertainty and allow for conditioning to “null” events. We also provide a characterisation of consistence of a partial assessment with a conditional submodular coherent risk measure. The latter amounts to test the solvability of a suitable sequence of linear systems.

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Author information

Authors and Affiliations

  1. Dip. Matematica e Informatica, University of Perugia, Perugia, Italy

    Giulianella Coletti

  2. Dip. Economia, University of Perugia, Perugia, Italy

    Davide Petturiti

  3. Dip. S.B.A.I., “La Sapienza” University of Rome, Rome, Italy

    Barbara Vantaggi

Authors
  1. Giulianella Coletti
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  2. Davide Petturiti
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  3. Barbara Vantaggi
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Corresponding author

Correspondence to Davide Petturiti .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Coletti, G., Petturiti, D., Vantaggi, B. (2018). Conditional Submodular Coherent Risk Measures. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-91476-3_20

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