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

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  • Föllmer Hans

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

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

Suggested Citation

  • Föllmer Hans, 2014. "Spatial risk measures and their local specification: The locally law-invariant case," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 79-101, March.
    • Handle: RePEc:bpj:strimo:v:31:y:2014:i:1:p:23:n:6
    DOI: 10.1515/strm-2013-5001
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    References listed on IDEAS

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