A unified approach to systemic risk measures via acceptance sets

Francesca Biagini; Jean‐Pierre Fouque; Marco Frittelli; Thilo Meyer‐Brandis

doi:10.1111/mafi.12170

journal article Feb 07, 2018

A unified approach to systemic risk measures via acceptance sets

Francesca Biagini

Jean‐Pierre Fouque Marco Frittelli Thilo Meyer‐Brandis

Mathematical Finance Vol. 29 No. 1 pp. 329-367 · Wiley

View at Publisher Save 10.1111/mafi.12170

Abstract

AbstractWe specify a general methodological framework for systemic risk measures via multidimensional acceptance sets and aggregation functions. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario‐dependent allocation). We also provide conditions that ensure monotonicity, convexity, or quasi‐convexity of our systemic risk measures.

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References

48

[1]

Acharya V. Pedersen L. Philippon T. &Richardson M.(2010).Measuring systemic risk. Working paper New York University Stern School of Business. 10.26509/frbc-wp-201002

[2]

Adrian T. &Brunnermeier M. K.(2011).Covar. Technical report National Bureau of Economic Research. 10.3386/w17454

[3]

10.1111/mafi.12051

[4]

Amini H. Filipovic D. &Minca A.(2014).Systemic risk with central counterparty clearing. Working paper. 10.2139/ssrn.2275376

[5]

Coherent Measures of Risk

Philippe Artzner, Freddy Delbaen, Jean‐Marc Eber et al.

Mathematical Finance 10.1111/1467-9965.00068

[6]

Battiston S. "Systemic risk in financial networks" Journal of Financial Management Markets and Institutions (2013)

[7]

Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk

Stefano Battiston, Domenico Delli Gatti, Mauro Gallegati et al.

Journal of Economic Dynamics and Control 10.1016/j.jedc.2012.04.001

[8]

Where the Risks Lie: A Survey on Systemic Risk

Sylvain Benoit, Jean-Edouard Colliard, Christophe Hurlin et al.

Review of Finance 10.1093/rof/rfw026

[9]

10.1016/j.jbankfin.2015.09.007

[10]

10.1080/14697680400020325

[11]

Boyd S. (2009)

[12]

Brunnermeier M. K. &Cheridito P.(2013).Measuring and allocating systemic risk. Preprint. 10.2139/ssrn.2372472

[13]

10.1016/j.jbankfin.2014.05.021

[14]

10.4310/cms.2015.v13.n4.a4

[15]

Cerreia‐Vioglio S. "Risk measures: Rationality and diversification" Mathematical Finance (2010)

[16]

10.1287/mnsc.1120.1631

[17]

10.1093/rfs/hhn081

[18]

10.1162/jeea.2005.3.2-3.556

[19]

10.1017/cbo9781139151184.018

[20]

10.1016/j.jfi.2014.02.003

[21]

Detering N. Meyer‐Brandis T. &Panagiotou K.(2016).Bootstrap percolation in directed and inhomogeneous random graphs. Preprint University of Munich.

[22]

Detering N. Meyer‐Brandis T. Panagiotou K. &Ritter D.(2016).Managing systemic risk in inhomogeneous financial networks. Preprint University of Munich.

[23]

10.1287/mnsc.47.2.236.9835

[24]

10.1137/16m1066087

[25]

10.1007/s007800200072

[26]

10.1515/9783110212075

[27]

10.1137/110841096

[28]

10.1017/cbo9781139151184

[29]

10.1017/cbo9781139151184.023

[30]

Complete duality for quasiconvex dynamic risk measures on modules of the L p -type

Marco Frittelli, Marco Maggis

Statistics & Risk Modeling 10.1515/strm-2013-1163

[31]

10.1016/s0378-4266(02)00270-4

[32]

10.1111/j.1467-9965.2006.00285.x

[33]

Gai P. &Kapadia S.(2010a).Contagion in financial networks. Bank of England Working Papers 383 Bank of England. 10.2139/ssrn.1577043

[34]

10.1098/rspa.2009.0410

[35]

Gleeson J. P. (2013)

[36]

10.1016/s1042-9573(03)00040-8

[37]

10.1016/j.spa.2016.01.002

[38]

10.1007/s11579-017-0210-3

[39]

A framework for assessing the systemic risk of major financial institutions

Xin Huang, Haibin Zhu

Journal of Banking & Finance 10.1016/j.jbankfin.2009.05.017

[40]

10.1007/978-3-319-33930-6

[41]

Hurd T. R. Cellai D. Melnik S. &Shao Q.(2014).Illiquidity and insolvency: A double cascade model of financial crises. Preprint available at arxiv.org/pdf/1310.6873. 10.2139/ssrn.2424877

[42]

Kley O. (2015)

[43]

Kromer E. Overbeck L. &Zilch K. A.(2013).Systemic risk measures on general probability spaces. Preprint University of Gießen Germany. 10.2139/ssrn.2268105

[44]

10.1016/j.jfs.2012.12.001

[45]

Measuring systemic risk: A risk management approach

Alfred Lehar

Journal of Banking & Finance 10.1016/j.jbankfin.2004.09.007

[46]

Pastore M. C.(2014).Systemic risk measures(Master thesis). University of Munich.

[47]

10.1287/mnsc.1120.1569

[48]

Weber S. "The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks" Probability, Uncertainty and Quantitative Risk (2017)

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78

Citations

48

References

Details

Published: Feb 07, 2018
Vol/Issue: 29(1)
Pages: 329-367
License: View

Authors

F

Francesca Biagini

Department of Mathematics University of Munich Munich Germany

J

Jean‐Pierre Fouque

Department of Statistics & Applied Probability University of California Santa Barbara CA

M

Marco Frittelli

Dipartimento di Matematica Università degli Studi di Milano Milano Italy

T

Thilo Meyer‐Brandis

Department of Mathematics University of Munich Munich Germany

Funding

National Science Foundation Award: DMS‐1107468

Cite This Article

Francesca Biagini, Jean‐Pierre Fouque, Marco Frittelli, et al. (2018). A unified approach to systemic risk measures via acceptance sets. Mathematical Finance, 29(1), 329-367. https://doi.org/10.1111/mafi.12170

A unified approach to systemic risk measures via acceptance sets

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