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Coherent Risk Measures and Upper Previsions

Renato Pelessoni () and Paolo Vicig
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Paolo Vicig: University of Trieste

Risk and Insurance from EconWPA

Abstract: 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.

Keywords: Coherent risk measure; imprecise prevision; Value-at-Risk; avoiding sure loss condition (search for similar items in EconPapers)
Date: 2002-01-22
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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