Article (Scientific journals)
Spatial Risk Measures and their Local Specification: The Locally Law-Invariant Case
Föllmer, Hans
2014In Statistics and Risk Modeling, 31 (1), p. 79–101
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Abstract :
[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
Disciplines :
Mathematics
Author, co-author :
Föllmer, Hans ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit ; Humboldt-Universität zu Berlin > Institut für Mathematik
Language :
English
Title :
Spatial Risk Measures and their Local Specification: The Locally Law-Invariant Case
Publication date :
March 2014
Journal title :
Statistics and Risk Modeling
ISSN :
2196-7040
Publisher :
Walter de Gruyter, Germany
Special issue title :
Systemic Risk
Volume :
31
Issue :
1
Pages :
79–101
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 13 February 2014

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