nach oben

Mathematics and Financial Economics

Erschienen in:

21.11.2019

Dual representations for systemic risk measures based on acceptance sets

verfasst von: Maria Arduca, Pablo Koch-Medina, Cosimo Munari

Erschienen in: Mathematics and Financial Economics | Ausgabe 1/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both “first allocate, then aggregate” and “first aggregate, then allocate” type. In both cases, we provide a detailed analysis of the corresponding systemic acceptance sets and their support functions. The same approach delivers a simple and self-contained proof of the dual representation of utility-based risk measures for univariate positions.

Vorheriger Artikel Compound Poisson models for weighted networks with applications in finance

Nächster Artikel Systemic credit freezes in financial lending networks

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Aliprantis, Ch.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide. Springer, Berlin (2006)

Ararat, Ç., Rudloff, B.: Dual representations for systemic risk measures. To appear in Math. Financ. Econ. arXiv:1607.03430 (2019)

Armenti, Y., Crépey, S., Drapeau, S., Papapantoleon, A.: Multivariate shortfall risk allocation and systemic risk. SIAM J. Financ. Math. 9, 90–126 (2018)MathSciNetCrossRefMATH

Artzner, Ph, Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)MathSciNetCrossRefMATH

Biagini, F., Fouque, J.P., Frittelli, M., Meyer-Brandis, T.: A unified approach to systemic risk measures via acceptance sets. Math. Finance 29, 329–367 (2019)MathSciNetCrossRefMATH

Biagini, F., Fouque, J., Frittelli, M., Meyer-Brandis, T.: On fairness of systemic risk measures. To appear in Finance Stoch. arXiv:1803.09898 (2019)

Biagini, S., Frittelli, M.: On the extension of the Namioka–Klee theorem and on the Fatou property for risk measures. In: Optimality and Risk: Modern Trends in Mathematical Finance, pp. 1–28. Springer (2009)

Burgert, C., Rüschendorf, L.: Consistent risk measures for portfolio vectors. Insur. Math. Econ. 38, 289–297 (2006)MathSciNetCrossRefMATH

Chen, C., Iyengar, G., Moallemi, C.C.: An axiomatic approach to systemic risk. Manag. Sci. 59, 1373–1388 (2013)CrossRef

10.

Delbaen, F.: Coherent risk measures on general probability spaces. In: Sandmann, K., Schönbucher, P.J. (eds.) Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, pp. 1–37. Springer, Berlin (2002)

11.

Delbaen, F., Owari, K.: Convex functions on dual Orlicz spaces. Positivity 23, 1051–1064 (2019)MathSciNetCrossRefMATH

12.

Dieudonné, J.: Sur la séparation des ensembles convexes. Math. Ann. 163(1), 1–3 (1966)MathSciNetCrossRef

13.

Edgar, G.A., Sucheston, L.: Stopping Times and Directed Processes. Cambridge University Press, Cambridge (1992)CrossRefMATH

14.

Ekeland, I., Galichon, A., Henry, M.: Comonotonic measures of multivariate risks. Math. Finance 22, 109–132 (2012)MathSciNetCrossRefMATH

15.

Ekeland, I., Schachermayer, W.: Law invariant risk measures on \(L^{\infty }({\mathbb{R}}^{d})\). Stat. Risk Model. 28, 195–225 (2011)MathSciNetCrossRef

16.

Farkas, W., Koch-Medina, P., Munari, C.: Measuring risk with multiple eligible assets. Math. Financ. Econ. 9, 3–27 (2015)MathSciNetCrossRefMATH

17.

Fan, K.: Minimax theorems. Proc. Natl. Acad. Sci. USA 39, 42 (1953)MathSciNetCrossRefMATH

18.

Feinstein, Z., Rudloff, B., Weber, S.: Measures of systemic risk. SIAM J. Financ. Math. 8, 672–708 (2017)MathSciNetCrossRefMATH

19.

Föllmer, H., Schied, A.: Stochastic Finance: An Introduction in Discrete Time. de Gruyter, Berlin (2016)CrossRefMATH

20.

Frittelli, M., Scandolo, G.: Risk measures and capital requirements for processes. Math. Finance 16, 589–612 (2006)MathSciNetCrossRefMATH

21.

Gao, N., Leung, D., Munari, C., Xanthos, F.: Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces. Finance Stoch. 22, 395–415 (2018)MathSciNetCrossRefMATH

22.

Gao, N., Leung, D., Xanthos, F.: Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures. Stud. Math. 249, 329–347 (2019)MathSciNetCrossRefMATH

23.

Gao, N., Munari, C.: Surplus-invariant risk measures. To appear in Math. Oper. Res., arXiv:1707.04949 (2017)

24.

Hamel, A.H., Heyde, F.: Duality for set-valued measures of risk. SIAM J. Financ. Math. 1, 66–95 (2010)MathSciNetCrossRefMATH

25.

Hamel, A.H., Heyde, F., Rudloff, B.: Set-valued risk measures for conical market models. Math. Financ. Econ. 5, 1–28 (2011)MathSciNetCrossRefMATH

26.

Jouini, E., Meddeb, M., Touzi, N.: Vector-valued coherent risk measures. Finance Stoch. 8, 531–552 (2004)MathSciNetMATH

27.

Kromer, E., Overbeck, L., Zilch, K.: Systemic risk measures over general measurable spaces. Math. Methods Oper. Res. 84, 323–357 (2016)MathSciNetCrossRefMATH

28.

Leung, D., Tantrawan, M.: On closedness of convex sets in Banach lattices. arXiv:1808.06747 (2018)

29.

Meyer-Nieberg, P.: Banach Lattices. Springer, Berlin (1991)CrossRefMATH

30.

Molchanov, I., Cascos, I.: Multivariate risk measures: a constructive approach based on selections. Math. Finance 26, 867–900 (2016)MathSciNetCrossRefMATH

31.

Rockafellar, R.T.: Conjugate Duality and Optimization. Society for Industrial and Applied Mathematics, Philadelphia (1974)CrossRefMATH

32.

Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (2009)MATH

33.

Rüschendorf, L.: Law invariant convex risk measures for portfolio vectors. Stat. Decis. 24, 97–108 (2006)MathSciNetMATH

34.

Zălinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)CrossRefMATH

Titel: Dual representations for systemic risk measures based on acceptance sets
verfasst von: Maria Arduca
Pablo Koch-Medina
Cosimo Munari
Publikationsdatum: 21.11.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics / Ausgabe 1/2021
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-019-00250-0

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 1/2021

Compound Poisson models for weighted networks with applications in finance

An optimization model for minimizing systemic risk

Systemic credit freezes in financial lending networks

An integrated model for fire sales and default contagion

Preface to the special issue on systemic risk and financial networks

How safe are central counterparties in credit default swap markets?