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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.

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Paper provided by EconWPA in its series Risk and Insurance with number 0201001.

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Length: 9 pages
Date of creation: 22 Jan 2002
Date of revision:
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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