# Birgit Rudloff

## Deputy Institute Chair

**Address:**

Welthandelsplatz 1, Building D4, Entrance A, 4th Floor

1020 Vienna, Austria

**Phone:** +43 1 31336-4731

**Office assistant:** Claudia Hoffmann

**Office hours:** by appointment

#### Research Interests

Multivariate risks, (dynamic) set-valued risk measures

Markets with transaction costs

Systemic risk measures

Incomplete preference relations

Algorithms to solve vector optimization problems

A set-valued Bellman's principle

Aumann integrals, stochastic differential inclusions

#### Short Vita

Vienna University of Economics and Business (2015 - present)

Full Professor since January 2017

Associate Professor (Febr.-Dec. 2016)

Assistant Professor (July 2015-Jan. 2016)

Habilitation in Financial Mathematics, January 2016Princeton University (2006-2015). Department of Operations Research and Financial Engineering, Assistant Professor

Vienna University of Technology, Financial and Actuarial Mathematics, Vienna, Austria (March-Aug. 2006);

IMPA (Instituto Nacional de Matematica Pura e Aplicada), Rio de Janeiro, Brazil (Feb. 2005-Jan. 2006);

Martin-Luther-University Halle-Wittenberg, Halle, Germany (1996-2006);

Ph.D. in Financial Mathematics, July 2006.

M.S. in Financial Mathematics, March 2002.

#### Research Group

**PostDocs **

Tobias Fissler (since 2019)

Kory Johnson (2020-2021)

Andrea Wagner (2016-2019), now Senior Lecturer at our institute

**PhD students**

Niklas Hey (since 2020)

Jana Hlavinová (since 2016)

Gabriela Kováčová (since 2016)

Firdevs Ulus (2011-2015), now Assistant Professor at Bilkent University

Çağın Ararat (2011-2015), now Assistant Professor at Bilkent University

Zach Feinstein (2010-2014), now Assistant Professor at Stevens Institute of Technology

#### Publications

**Editorial Work**

Set Optimization and Applications in Finance - The State of the Art. From Set-Relations to Set-Valued Risk Measures.

(co-edited with A.H. Hamel, F. Heyde, A. Löhne, C. Schrage).

Springer Proceedings in Mathematics & Statistics, Vol. 151, Springer, 2015.

331 pages. ISBN: 978-3-662-48668-9

**Submitted papers and preprints**

G. Kováčová, B. Rudloff, I. Cialenco:

**Acceptability maximization.**[preprint] at arXiv.

Submitted for publication.T. Fissler, R. Frongillo, J. Hlavinová, B. Rudloff:

**Forecast Evaluation of Quantiles, Prediction Intervals, and other Set-Valued Functionals.**[preprint] at arXiv.

Submitted for publication.Z. Feinstein, B. Rudloff:

**Scalar multivariate risk measures with a single eligible asset.**[preprint] at arXiv.

Submitted for publication.Z. Feinstein, B. Rudloff:

**Time consistency for scalar multivariate risk measures**[preprint] at arXiv.

Submitted for publication.A. Hamel, B. Rudloff, Z. Zhou:

**Robust no arbitrage and the solvability of vector-valued utility maximization problems.**[preprint] at arXiv.

Submitted for publication.

**Peer-reviewed publication**

Z. Feinstein, B. Rudloff, J. Zhang (2020):

**Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums.**[pdf] at arXiv.

Forthcoming in Mathematics of Operations Research.T. Fissler, J. Hlavinová, B. Rudloff (2021):

**Elicitability and Identifiability of Systemic Risk Measures.**[pdf] at arXiv.*Finance and Stochastics*25(1), 133–165.G. Kováčová, B. Rudloff (2020):

**Time consistency of the mean-risk problem.**[pdf] at arXiv.

Forthcoming in Operations Research.B. Rudloff, F. Ulus (2020):

**Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization.**[pdf] at arXiv.

Forthcoming in*Mathematics and Financial Economics*.Ç. Ararat, B. Rudloff (2020):

**Dual representations for systemic risk measures.**[pdf] at arXiv.*Mathematics and Financial Economics*14(1), 139-174Z. Feinstein, W. Pang, B. Rudloff, E. Schaanning, S. Sturm, M. Wildman (2018):

**Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities.**[pdf] at arXiv.*SIAM Journal on Financial Mathematics*9 (4), 1137-1325.Z. Feinstein, B. Rudloff (2018):

**A Supermartingale Relation for Multivariate Risk Measures.**[pdf] at arXiv.*Quantitative Finance*18 (12), 1971-1990.*Z. Feinstein, B. Rudloff, S. Weber (2017):***Measures of systemic risk.**[pdf] at arXiv.*SIAM Journal on Financial Mathematics*8 (1), 672-708.*Ç. Ararat, A. Hamel, B. Rudloff (2017):***Set-valued shortfall and divergence risk measures.**[pdf] at arXiv.*International Journal of Theoretical and Applied Finance*20 (5) 1750026*B. Rudloff, F. Ulus, R. Vanderbei (2017):***A parametric simplex algorithm for linear vector optimization problems.**[pdf] at arXiv.*Mathematical Programming SERIES A*163 (1), 213-242.*Z. Feinstein, B. Rudloff (2017):***A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle.**[pdf] at arXiv.*Journal of Global Optimization*68 (1), 47–69.*Z. Feinstein, B. Rudloff (2015):***Multi-portfolio time consistency for set-valued convex and coherent risk measures.**[pdf] at arXiv.*Finance and Stochastics*19 (1), 67-107.*A. Löhne, B. Rudloff (2015):***On the dual of the solvency cone.**[pdf] at arXiv.*Discrete Applied Mathematics*186, 176-185.*Ç. Ararat, B. Rudloff (2015):***A characterization theorem for Aumann integrals.**[pdf] at arXiv.*Set-Valued and Variational Analysis*23 (2), 305-318.*A. Hamel, F. Heyde, A. Löhne, B. Rudloff, C. Schrage (2015):***Set optimization - a rather short introduction.**(76 pages) [pdf] at arXiv.

In: A.H. Hamel, F. Heyde, A. Löhne, B. Rudloff, C. Schrage (eds.): Set Optimization and Applications in Finance - The State of the Art, Springer PROMS series, Vol. 151, 65-141. ISBN: 978-3-662-48668-9*Z. Feinstein, B. Rudloff (2015):***A comparison of techniques for dynamic multivariate risk measures.**[pdf] at arXiv.

In: A.H. Hamel, F. Heyde, A. Löhne, B. Rudloff, C. Schrage (eds.): Set Optimization and Applications in Finance - The State of the Art, Springer PROMS series, Vol. 151, 3-41. ISBN: 978-3-662-48668-9*A. Löhne, B. Rudloff (2014):***An algorithm for calculating the set of superhedging portfolios in markets with transaction costs.**[pdf] at arXiv.*International Journal of Theoretical and Applied Finance*17 (2) 1450012 (33 pages).

An implementation of**Benson's algorithm**(by A. Löhne) used to solve the linear vector optimization problems arising in the above paper can be downloaded here [Benson]*A. Löhne, B. Rudloff, F. Ulus (2014):***Primal and dual approximation algorithms for convex vector optimization problems.**[pdf] at arXiv.*Journal of Global Optimization*60 (4) 713-736.*B. Rudloff, A. Street, D. Valladao (2014):***Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences.**[pdf] at optimization online.*European Journal of Operational Research*234 (3), 743-750.*A. Hamel, A. Löhne, B. Rudloff (2014):***Benson type algorithms for linear vector optimization and applications.**[pdf] at arXiv*Journal of Global Optimization*59 (4), 811-836.

A MatLab as well as a C implementation (by A. Löhne) can be downloaded here [Benson]*A. Hamel, B. Rudloff, M. Yankova (2013):***Set-valued average value at risk and its computation.**[pdf] at arXiv.*Mathematics and Financial Economics*7 (2), 229-246.*Z. Feinstein, B. Rudloff (2013):***Time consistency of dynamic risk measures in markets with transaction costs.**[pdf] at arXiv.*Quantitative Finance*13 (9), 1473-1489.*A. Hamel, F. Heyde, B. Rudloff (2011):***Set-valued risk measures for conical market models.**[pdf] at arXiv.*Mathematics and Financial Economics*5 (1), 1 - 28.*B. Rudloff, I. Karatzas (2010):***Testing Composite Hypotheses via Convex Duality.**[pdf] at arXiv.*Bernoulli*16 (4), 1224 - 1239.*B. Rudloff (2009):***Coherent Hedging in Incomplete Markets.***Quantitative Finance*9 (2), 197 - 206.*B. Rudloff, J. Sass, R. Wunderlich (2008):***Entropic Risk Constraints for Utility Maximization.**

In: Chr. Tammer, F. Heyde (eds.): Festschrift in Celebration of Prof. Dr. Wilfried Grecksch's 60th Birthday. Shaker Verlag, Aachen, 149 - 180. ISBN 978-3-8322-7500-6.*A. Hamel, B. Rudloff (2008):***Continuity and Finite-Valuedness of Set-Valued Risk Measures.**

In: Chr. Tammer, F. Heyde (eds.): Festschrift in Celebration of Prof. Dr. Wilfried Grecksch's 60th Birthday. Shaker Verlag, Aachen, 49 - 64. ISBN 978-3-8322-7500-6.*B. Rudloff (2007):***Convex Hedging in Incomplete Markets.**[pdf] at arXiv.*Applied Mathematical Finance*14 (5), 437 - 452.*B. Rudloff (2005):***A Generalized Neyman-Pearson Lemma for Hedge Problems in Incomplete Markets.**

Proceedings of the Workshop*Stochastische Analysis*, 241 - 250. ISSN 1612-5665.*B. Rudloff (2005):***Hedging with Convex Risk Measures.**

In: N. Kolev, P. Morettin (eds.): Proceedings of the Second Brazilian Conference on Statistical Modelling in Insurance and Finance, ISBN 85-88697-07-6.

**Theses**

**Hedging in Incomplete Markets and Testing Compound Hypotheses via Convex Duality.**

PhD Thesis, Martin-Luther-University Halle-Wittenberg, 2006.

Advisor: Prof. W. Grecksch.**Valuation of Default Correlations and Application to Pricing synthetic CDO's.**

Master Thesis (Diplomarbeit), Martin-Luther-University Halle-Wittenberg, 2002.

[in german: Ein Modell zur Berechnung von Ausfallkorrelationen und dessen Anwendung auf die Bewertung synthetischer CDOs]

Advisor: Prof. W. Grecksch.