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A Representation of Risk Measures

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  • Massimiliano AMARANTE

Abstract

We provide a representation theorem for risk measures satisfying (i) monotonicity; (ii) positive homogeneity; and (iii) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition, sub-additive; see Artzner et al.

Suggested Citation

  • Massimiliano AMARANTE, 2013. "A Representation of Risk Measures," Cahiers de recherche 11-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:11-2013
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    References listed on IDEAS

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    Cited by:

    1. Amarante, Massimiliano & Ghossoub, Mario, 2021. "Aggregation of opinions and risk measures," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Felix-Benedikt Liebrich, 2024. "Risk sharing under heterogeneous beliefs without convexity," Finance and Stochastics, Springer, vol. 28(4), pages 999-1033, October.

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    More about this item

    Keywords

    risk measures; capacity; Choquet integral;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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