Spatial risk measures and their local specification: The locally law-invariant case
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Hans Föllmer
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
©2014 Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Special Issue on Systemic Risk
- Foreword
- Central clearing of OTC derivatives: Bilateral vs multilateral netting
- Optimal control of interbank contagion under complete information
- On dependence consistency of CoVaRand some other systemic risk measures
- Spatial risk measures and their local specification: The locally law-invariant case
- Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type
Artikel in diesem Heft
- Frontmatter
- Special Issue on Systemic Risk
- Foreword
- Central clearing of OTC derivatives: Bilateral vs multilateral netting
- Optimal control of interbank contagion under complete information
- On dependence consistency of CoVaRand some other systemic risk measures
- Spatial risk measures and their local specification: The locally law-invariant case
- Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type
