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Coherent Risk Measures and Upper Previsions


  • Renato Pelessoni

    (University of Trieste)

  • Paolo Vicig

    (University of Trieste)


In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. We also show that Value-at-Risk does not necessarily satisfy a weaker notion of coherence called ‘avoiding sure loss’ (ASL), and discuss both sufficient conditions for VaR to avoid sure loss and ways of modifying VaR into a coherent risk measure.

Suggested Citation

  • Renato Pelessoni & Paolo Vicig, 2002. "Coherent Risk Measures and Upper Previsions," Risk and Insurance 0201001, EconWPA.
  • Handle: RePEc:wpa:wuwpri:0201001
    Note: Type of Document - pdf; prepared on PC - TEX; pages: 9 ; figures: none. Presented at the 2nd International Symposium on Imprecise Probabilities and Their Applications, Ithaca, New York, 2001

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    References listed on IDEAS

    1. Doherty, N A & Tinic, S M, 1981. "Reinsurance under Conditions of Capital Market Equilibrium: A Note," Journal of Finance, American Finance Association, vol. 36(4), pages 949-953, September.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
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    Cited by:

    1. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.

    More about this item


    Coherent risk measure; imprecise prevision; Value-at-Risk; avoiding sure loss condition;

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