2014 - 2015: Associate Prof., University of Vienna
2004-2014:
PostDoc / Project Assistent / Assistent Prof., University of Vienna / TU
Vienna, extended research visits at OSU (Columbus), MSRI (Berkeley)
2013: Substitute Professor, Bonn University
2010: Habilitation in Mathematics, University of Vienna
Alternative Civil Service
2004: Doctorate in Mathematics, TU Vienna
2003: Diploma in Mathematics, TU Vienna
Projects and Prizes
2014: START-Prize (Awarded by the Austrian Science Fund FWF, 1.000.000 EURO)
2012: Prize of the Austrian Mathematical Society
2003: Award for the best Master's thesis in Mathematics, Austrian Mathematical Society
Causal Transport in Discrete Time and Applications. with J. Backhoff, A. Zalashko, and Y. Lin.
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Publications
Pathwise Super-Hedging via Vovk's Outer Measure. with M. Huesmann, A. Cox, N. Perkowski and D. Proemel Finance and Stochastics, to appear
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Optimal Transport and Skorokhod Embedding. with A. Cox and M. Huesmann. Invent. Math., to appear
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A land of monotone plenty. with C. Griessler. Annali della SNS
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Monotone Martingale Transport Plans and Skorokhod Embedding. with N. Touzi and P. Henry-Labordere. SPA, to appear
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Root to Kellerer. with M. Huesmann and F. Stebegg. Sem. de Prob., to appear
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Complete Duality for
Martingale Optimal Transport on the Line. with M. Nutz and N. Touzi. Ann. Probab., to appear
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A Model-free Version of the Fundamental Theorem of Asset Pricing and the Super-Replication Theorem.,
with B. Acciaio, F. Penkner, W. Schachermayer. Math. Finance, 26 (2016), no. 2, 233–251.
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On a problem of optimal transport under marginal martingale constraints. with N. Juillet.
Ann. Probab., 44 (2016), no. 1, 42–106. [pdf]
Martingale Inequalities and Deterministic Counterparts. with M. Nutz. Electron. J. Probab. Electron. J. Probab. 19 (2014), no. 95, 15 pp.
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Pathwise Versions of the Burkholder-Davis-Gundy Inequalities. with P. Siorpaes. Bernoulli, 21 (2015), no. 1, 360–373.
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Riemann-integration and a Simple Proof of the Bichteler-Dellacherie Theorem. with P. Siorpaes.
Stochastic Process. Appl. 124 (2014), no. 3, 1226-1235. [pdf]
Cyclical Monotonicity and the Ergodic Theorem. Ergodic Theory Dynam. Systems, 35 (2015), no. 3, 710–713.
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Model-independent Bounds for Option Prices: A Mass Transport Approach,
with P. Henry-Labordaire and F. Penkner., Finance Stoch. 17 (2013), no. 3, 477-501.
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A Trajectorial Interpretation of Doob's Martingale Inequalities.,
with B. Acciaio, F. Penkner, W. Schachermayer, and J. Temme. Ann. Appl. Probab. 23 (2013), no. 4, 1494-1505.
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A short Proof of the Doob-Meyer Theorem,
with W. Schachermayer, B. Veliyev. Stochastic Process. Appl. 122 (2012), no. 4, 1204-1209.
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Duality for rectified cost functions,
with A. Pratelli Calc. Var. Partial Differential Equations 45 (2012), no. 1-2, 27-41.
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A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage,
with W. Schachermayer, B. Veliyev. Ann. Probab. 39 (2011), no. 6, 2424-2440.
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A general duality theorem for the Monge Kantorovich transport problem,
with C. Leonard, W. Schachermayer. Studia Math. 209 (2012), no. 2, 151-167.
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A generalized dual maximizer for the Monge--Kantorovich transport problem,
with C. Leonard, W. Schachermayer. ESAIM Probab. Stat. 16 (2012), 306-323.
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On the duality theory for the Monge-Kantorovich transport problem,
with C. Leonard, W. Schachermayer.
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Utility Maximization, Risk Aversion, and Stochastic Dominance, Math. Financ. Econ. 6 (2012), no. 1, 1-13.
with J. Muhle-Karbe, J. Temme.
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Is the minimum value of an option on variance generated by local
volatility?,
with P. Friz, S. Sturm. SIAM J. Financial Math. , 2, 213-220, (2010).
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Transfinite Approximation of Hindman's Theorem,
with H. Towsner. Israel J. Math. 191 (2012), no. 1, 41-59.
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An Ultrafilter Approach to Jin's Theorem.
Israel J. Math. 185 (2011), 369-374. [pdf]
Sumset Phenomenon in Amenable Groups,
with V. Bergelson and A. Fish, Adv. Math. 223 (2010), no. 2, 416-432.
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Duality for Borel Measurable Cost Functions,
with W. Schachermayer, Trans. Amer. Math. Soc., 363, no. 8, 4203-4224, (2011).
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Clones from ideals,
with M. Goldstern, L. Heindorf and M. Pinsker,
Internat. Internat. J. Algebra Comput. 19 (2009), no. 3, 397-421.
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Optimal and better transport,
with M. Goldstern, G. Maresch and W. Schachermayer, J. Funct. Anal. 256 (2009), no. 6, 1907-1927.
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Arithmetic progressions in abundance by combinatorial means, Proc. Amer. Math. Soc. 137 (2009), no. 12, 3981-3983.
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Solvability of Rado systems in D-sets,
with V. Bergelson, T. Downarowicz and A. Fish, Topology Appl., to appear.
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A Variant of the Hales-Jewett theorem, Bull. Lond. Math. Soc. 360., 40 (2008), no. 2, 210-216.
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Some new results in multiplicative and additive
Ramsey Theory,
with V. Bergelson, N. Hindman and D. Strauss, Trans. Amer. Math. Soc. 360. (2008) no. 2, 819-847.
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Strong characterizing sequences of countable
groups, J. of Number Theory 127 (2007), no. 2, 145-152.
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A multidimensional Central Sets Theorem,
Combin., Probab. and Comput. 15 (2006), no. 6, 807-814.
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Multiplicative structures in additively large sets,
with V. Bergelson, N. Hindman and D. Strauss,
J. Combin. Theory Ser. A 113 (2006) no. 7, 1219-1242.
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Sequences and filters of characters characterizing subgroups
of compact abelian groups,
with C. Steineder and R. Winkler,
Topology Appl. 153 (2006), no. 11, 1682-1695.
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