Affiliation:
1. Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany
Abstract
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
Subject
Statistics, Probability and Uncertainty,Modeling and Simulation,Statistics and Probability
Cited by
11 articles.
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