Faculty of Mathematics

Mathias Beiglboeck

Mathias Beiglboeck Office: 1090 Wien, Oskar Morgensternplatz 1, 6. floor Phone: +43 1 4277 50634 Email: mathias.beiglboeck@univie.ac.at Office Hours: Thursday 14:00-15:00

Research

Preprints

• A Probabilistic View on the Adapted Wasserstein Distance, with S. Pflügl, S. Schrott [pdf]
• Change of numeraire for weak martingale transport, with G. Pammer and L. Riess [pdf]
• The Knothe-Rosenblatt distance and its induced topology, with G. Pammer and A. Posch [pdf]
• Representing general stochastic processes as martingale laws, with G. Pammer, S. Schrott, and X. Zhang [pdf]
• The structure of martingale Benamou-Brenier in multiple dimensions, with J. Backhoff, W. Schachermayer and B. Tschiderer [pdf]
• The geometry of financial institutions -- Wasserstein clustering of financial data, with L. Riess, J. Temme, A. Wolf, and J. Backhoff [pdf]
• Denseness of adapted processes among causal couplings, with D. Lacker [pdf]

Publications

• The Wasserstein space of filtered processes, with D. Bartl and G. Pammer , J. Eur. Math. Soc., to appear, [pdf]
• The most exciting game, with J. Backhoff, Electron. Commun. Probab., 2024, [pdf]
• Denseness of biadapted Monge mappings, with G. Pammer and S. Schrott AIHP, 2023 [pdf]
• Faking Brownian motion with continuous Markov martingales, with G. Lowther, G. Pammer, W. Schachermayer Fin. Stoch, 2023 [pdf]
• A non-linear monotonicity principle and applications to Schrödinger type problems, with J. Backhoff-Veraguas and G. Conforti, Bull. of the LMS, 2022 [pdf]
• Stability of the Weak Martingale Optimal Transport Problem, with B. Jourdain, W. Margheriti, G. Pammer, AAP, 2023 [pdf]
• Approximation of martingale couplings on the line in the weak adapted topology, with B. Jourdain, W. Margheriti, G. Pammer, PTRF, 2022 [pdf]
• Estimating processes in adapted Wasserstein distance. with D. Bartl, J. Backhoff and J. Wiesel, Ann. Appl. Probab. 32, 2022 [pdf]
• Fine Properties of the Optimal Skorokhod Embedding Problem, with M. Nutz and F. Stebegg, J. Eur. Math. Soc., 2022 [pdf]
• The potential of the shadow measure. with D. Hobson and D. Norgilas, Electron. Commun. Probab., 2022, [pdf]
• From Bachelier to Dupire via Optimal Transport, with G. Pammer, W. Schachermayer, Fin. Stoch, 2022 [pdf]
• Weak transport for non-convex costs and model-independence in a fixed-income market, with B. Acciaio, G. Pammer, Math. Finance, 2021 [pdf]
• Rapid antigen tests for SARS-CoV-2: their sensitivity, benefits for epidemic control, and use in Austrian schools, with J. Polechova, K. Johnson, P. Payne, Alex Crozier, s P. Plevka, E. Schernhammer Journal of Clinical Epidemiology 145, 2022 14–19, [pdf]
• Robust models of disease heterogeneity and control, with application to the SARS-CoV-2 epidemic, with A. Grass, K. Johnson, J. Polechova, D. Toneian, PLOS Glob Public Health. 2(5); 2022 [pdf]
• Shadow Couplings, with N. Juillet , Transactions of the AMS, 2021 [pdf]
• Analysis of the specificity of the SD Biosensor Standard Q Ag-Test based on Slovak mass testing data, with M. Hledík, Polechova, A. Herdina, R. Strassl, M. Posch PLOS ONE, 2021 [pdf]
• Disease Momentum: Estimating the Reproduction Number in the Presence of Superspreading, with K. Johnson, M. Eder, A. Grass, J. Hermisson, G. Pammer, J. Polechova, D. Toneian, B. Woelfl, Infectious Disease Modelling, 2021, [pdf]
• All adapted topologies are equal, with J. Backhoff, D. Bartl, and M. Eder, PTRF, 2020 [pdf]
• Existence, duality and cyclical monotonicity for weak transport costs with J. Backhoff and G. Pammer Calc. Var. PDE, 2019 [pdf]
• Martingale Benamou-Brenier: a Probabilistic Perspective. with J. Backhoff, M. Huesmann and S. Kaellblad. Ann. Prob., 2020 [pdf]
• Adapted Wasserstein distances and stability in mathematical finance. with J. Backhoff, D. Bartl, and M. Eder. Finance and Stochastics, 2020 [pdf]
• Weak monotone rearrangement on the line. with J. Backhoff and G. Pammer ECP 2020 [pdf]
• The geometry of multi-marginal Skorokhod Embedding. with A. Cox and M. Huesmann. PTRF, 2020 [pdf]
• Dual attainment for the martingale transport problem. with T. Lim and J. Obloj. Bernoulli, 2019 [pdf]
• Geometry of Distribution-Constrained Optimal Stopping Problems. with M. Eder, C. Elgert, and U. Schmock PTRF, 2018 [pdf]
• Fundamental properties of process distancess. with J. Backhoff, M. Eder, and A. Pichler , SPA, 2019 [pdf]
• Causal Transport in Discrete Time and Applications. with J. Backhoff, A. Zalashko, and Y. Lin. SIAM Journal on Optimization, 2018 [pdf]
• Optimal Transport and Skorokhod Embedding. with A. Cox and M. Huesmann. Invent. Math., 2018 [pdf]
• Pathwise Super-Hedging via Vovk's Outer Measure. with M. Huesmann, A. Cox, N. Perkowski and D. Proemel Finance and Stochastics, 2018 [pdf]
• A land of monotone plenty. with C. Griessler. Annali della SNS, 2019 [pdf]
• Monotone Martingale Transport Plans and Skorokhod Embedding. with N. Touzi and P. Henry-Labordere. SPA, 2016 [pdf]
• Root to Kellerer. with M. Huesmann and F. Stebegg. Sem. de Prob., 2017 [pdf]
• Complete Duality for Martingale Optimal Transport on the Line. with M. Nutz and N. Touzi. Ann. Probab., 2016 [pdf]
• 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. [pdf]
• 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. [pdf]
• Pathwise Versions of the Burkholder-Davis-Gundy Inequalities. with P. Siorpaes. Bernoulli, 21 (2015), no. 1, 360–373. [pdf]
• 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. [pdf]
• 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. [pdf]
• 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. [pdf]
• A short Proof of the Doob-Meyer Theorem, with W. Schachermayer, B. Veliyev. Stochastic Process. Appl. 122 (2012), no. 4, 1204-1209. [pdf]
• Duality for rectified cost functions, with A. Pratelli Calc. Var. Partial Differential Equations 45 (2012), no. 1-2, 27-41. [pdf]
• 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. [pdf]
• A general duality theorem for the Monge Kantorovich transport problem, with C. Leonard, W. Schachermayer. Studia Math. 209 (2012), no. 2, 151-167. [pdf]
• A generalized dual maximizer for the Monge--Kantorovich transport problem, with C. Leonard, W. Schachermayer. ESAIM Probab. Stat. 16 (2012), 306-323. [pdf]
• On the duality theory for the Monge-Kantorovich transport problem, with C. Leonard, W. Schachermayer. [pdf]
• Utility Maximization, Risk Aversion, and Stochastic Dominance, Math. Financ. Econ. 6 (2012), no. 1, 1-13. with J. Muhle-Karbe, J. Temme. [pdf]
• 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). [pdf]
• Transfinite Approximation of Hindman's Theorem, with H. Towsner. Israel J. Math. 191 (2012), no. 1, 41-59. [pdf]
• 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. [pdf]
• Duality for Borel Measurable Cost Functions, with W. Schachermayer, Trans. Amer. Math. Soc., 363, no. 8, 4203-4224, (2011). [pdf]
• Clones from ideals, with M. Goldstern, L. Heindorf and M. Pinsker, Internat. Internat. J. Algebra Comput. 19 (2009), no. 3, 397-421. [pdf]
• Optimal and better transport, with M. Goldstern, G. Maresch and W. Schachermayer, J. Funct. Anal. 256 (2009), no. 6, 1907-1927. [pdf]
• Arithmetic progressions in abundance by combinatorial means, Proc. Amer. Math. Soc. 137 (2009), no. 12, 3981-3983. [pdf]
• Solvability of Rado systems in D-sets, with V. Bergelson, T. Downarowicz and A. Fish, Topology Appl., to appear. [pdf]
• A Variant of the Hales-Jewett theorem, Bull. Lond. Math. Soc. 360., 40 (2008), no. 2, 210-216. [pdf]
• 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. [pdf]
• Strong characterizing sequences of countable groups, J. of Number Theory 127 (2007), no. 2, 145-152. [pdf]  
• A multidimensional Central Sets Theorem, Combin., Probab. and Comput. 15 (2006), no. 6, 807-814. [pdf]
• 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. [pdf]
• 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. [pdf]

Teaching WS2024/25

250037-1 VO Finanzmathematik (Bachelor)

Teaching WS2023/24

lecture notes (stochastic mass transport), SS 2024

• notes (under construction) [pdf]

Teaching WS2023/24

250127 VO Stochastik für das Lehramt

Teaching SS2023

VO Wahrscheinlichkeitstheorie und Grundzüge der Statistik

Mini CV

• Born 1980

Jobs and Education

• 2018-: Prof., University of Vienna
• 2016-2018: Prof., TU Vienna
• fall 2015: paternity leave
• 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

• 2024 - : OeNB-Anniversary-Fund Project 18983, The landscape of financial institutions - geometric representation by entropic and adapted transport, (250.000 EURO)
• 2023 -: Mentor in Daniel Bartl's Esprit-Project (280.000 EURO)
• 2022 - : FWF-Project, Transport Approach to Mimicking Processes, (400.000 EURO)
• 2014-2022: START-Prize (Awarded by the Austrian Science Fund FWF, 1.000.000 EURO)
• 2013: FWF-Project (Model Independence and Transport) (430.000 EURO)
• 2012: Prize of the Austrian Mathematical Society
• 2009-2013: FWF-Project (200.000 EURO)
• 2003: Award for the best Master's thesis in Mathematics, Austrian Mathematical Society