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A representation of risk measures

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  • Massimiliano Amarante

    (Université de Montréal et CIREQ)

Abstract

We provide a representation theorem for risk measures satisfying (1) monotonicity, (2) positive homogeneity and (3) 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. in Math Finance 9:203–228, 1999).

Suggested Citation

  • Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    • Handle: RePEc:spr:decfin:v:39:y:2016:i:1:d:10.1007_s10203-016-0170-8
    DOI: 10.1007/s10203-016-0170-8
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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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