Spatial risk measures and their local specification: The locally law-invariant case

Föllmer Hans ()
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Föllmer Hans: Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany

Statistics & Risk Modeling, 2014, vol. 31, issue 1, 79-101

Abstract: We consider convex risk measures in a spatial setting, where the outcome of a financial position depends on the states at different nodes of a network. In analogy to the theory of Gibbs measures in Statistical Mechanics, we discuss the local specification of a global risk measure in terms of conditional local risk measures for the single nodes of the network, given their environment. Under a condition of local law invariance, we show that a consistent local specification must be of entropic form. Even in that case, a global risk measure may not be uniquely determined by the local specification, and this can be seen as a source of “systemic risk”, in analogy to the appearance of phase transitions in the theory of Gibbs measures

Keywords: Convex risk measure; spatial risk measure; entropic risk measure; phase transition; systemic risk; Convex risk measure; spatial risk measure; entropic risk measure; phase transition; systemic risk (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/strm-2013-5001

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