Systemic Risk Measures on General Measurable Spaces

30 Pages Posted: 22 May 2013 Last revised: 29 May 2016

See all articles by Eduard Kromer

Eduard Kromer

University of California, Berkeley

Ludger Overbeck

University of Giessen

Katrin Zilch

University of Giessen

Date Written: May 29, 2016

Abstract

In view of the recent financial crisis systemic risk has become a very important research object. It is of significant importance to understand what can be done from a regulatory point of view to make the financial system more resilient to global crises. Systemic risk measures can provide more insight on this aspect. The study of systemic risk measures should support central banks and financial regulators with information that allows for better decision making and better risk man- agement. For this reason this paper studies systemic risk measures on locally convex-solid Riesz spaces. In our work we extend the axiomatic approach to systemic risk, as introduced in Chen et al. (2013), in different directions. One direction is the introduction of systemic risk measures that do not have to be positively homogeneous. The other direction is that we allow for a general measurable space whereas in Chen et al. (2013) only a finite probability space is considered. This extends the scope of possible loss distributions of the components of a financial system to a great extent and introduces more flexibility for the choice of suitable systemic risk measures.

Keywords: systemic risk measure, aggregation function, locally convex-solid Riesz spaces, decomposition, dual representation, risk attribution

JEL Classification: D81

Suggested Citation

Kromer, Eduard and Overbeck, Ludger and Zilch, Katrin, Systemic Risk Measures on General Measurable Spaces (May 29, 2016). Available at SSRN: https://ssrn.com/abstract=2268105 or http://dx.doi.org/10.2139/ssrn.2268105

Eduard Kromer

University of California, Berkeley ( email )

Evans Hall
Berkeley, CA 3860 94720
United States

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Katrin Zilch (Contact Author)

University of Giessen ( email )

Department of Mathematics
Arndtstr. 2
Giessen, 35392
Germany

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