Reference : Spatial Risk Measures and their Local Specification: The Locally Law-Invariant Case
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/15716
Spatial Risk Measures and their Local Specification: The Locally Law-Invariant Case
English
Föllmer, Hans mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit > ; Humboldt-Universität zu Berlin > Institut für Mathematik]
Mar-2014
Statistics & Risk Modeling
31
1
Systemic Risk
79–101
Yes (verified by ORBilu)
International
2193-1402
2196-7040
[en] 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
http://hdl.handle.net/10993/15716
10.1515/strm-2013-5001

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