Prof. Dr. Wolfgang Stummer
Professur für Mathematik
Professorinnen und Professoren
Adresse
Cauerstraße 11 91058 Erlangen
Kontakt
Raum: 02.330
Cauerstraße 11
91058 Erlangen
Deutschland
Telefon: +49 9131 85-67081
Faxnummer: +49 9131 85-67089
Office hours (Sprechstunde)
- in der Vorlesungszeit: Mittwoch, 17 bis 18 Uhr.
- in der vorlesungsfreien Zeit: nach Vereinbarung (per Email).
- im eingeschränkten Universitätsbetrieb (z.B. bedingt durch COVID-19 oder andere Pandemien): per Email.
Research fields
Stochastic Processes, Probability Theory, Statistics, Information Theory,
Machine Learning, Artificial Intelligence, Data Analytics, Uncertainty Quantification,
and their interdisciplinary applications to:
- Finance, Econometrics, Business, Economics
- Decision Making and Risk Analysis
- Life Sciences (Physics, Biology, Epidemiology, Medicine, Climate Research)
- Sustainable Development Goals (SDGs)
- Signal Processing
- Recognition of Patterns and Structures (within these fields)
- Big Data Analytics
| Degree |
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| Positions |
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| Selected invited visits and invited (conference) talks |
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| M. Broniatowski, W. Stummer: Foundations of bare-simulation optimization of distances. Annals of Applied Probability 36(3), June 2026, pp. 2237-2291, https://doi.org/10.1214/25-AAP2278 (open access). The corresponding supplement (30 pages) can be found at https://doi.org/10.1214/25-AAP2278SUPP (open access). | |
| P. Bertrand, W. Stummer: Some smooth divergences for ℓ1−approximations. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2025, Part I, Lecture Notes in Computer Science 16033, Springer, 2026, pp. 359–368. https://doi.org/10.1007/978-3-032-03918-7_37. See also arXiv:2511.00219 and HAL:05142505v1 (8 pages) | |
| P. Bertrand, M. Broniatowski, W. Stummer: Hybrid random concentrated optimization without convexity assumption. arXiv:2503.23864v3 (27 pages) | |
| M. Broniatowski, W. Stummer: Some theoretical foundations of bare-simulation optimization of some directed distances between fuzzy sets respectively basic belief assignments. Entropy 26, 312, 2024. https://doi.org/10.3390/e26040312 | |
| M. Broniatowski, W. Stummer: A precise bare simulation approach to the minimization of some distances. II. Further Foundations. arXiv:2402.08478v1 (77 pages) | |
| M. Broniatowski, W. Stummer: A precise bare simulation approach to the minimization of some distances. I. Foundations.IEEE Transactions on Information Theory 69(5), May 2023, pp. 3062-3120, https://doi.org/10.1109/TIT.2022.3215496.See also arXiv:2107.01693v3 (71 pages).An earlier, extended, differently structured version can be found under the slightly different title „A precise bare simulation approach to the minimization of some distances. Foundations“ at arXiv:2107.01693v1 (typo-corr. v2), 2021, 94 pages. | |
| M. Broniatowski, W. Stummer: On a cornerstone of Bare-Simulation Distance/Divergence Optimization. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2023, Part I, Lecture Notes in Computer Science 14071, Springer, 2023, pp. 105–116. https://doi.org/10.1007/978-3-031-38271-0_11 | |
| M. Broniatowski, W. Stummer: A Unifying Framework for Some Directed Distances in Statistics. In: F. Nielsen, A.S.R. Srinivasa Rao and C.R. Rao (eds.), Handbook of Statistics Vol. 46, Academic Press/Elsevier, 2022, pp. 145-223. https://doi.org/10.1016/bs.host.2022.03.007.See also arxiv:2203.00863 | |
| W. Stummer: Optimal transport with some directed distances. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2021, Lecture Notes in Computer Science 12829, Springer, 2021, pp. 829–840. https://doi.org/10.1007/978-3-030-80209-7_89 | |
| N.B. Kammerer, W. Stummer: Some dissimilarity measures of branching processes and optimal decision making in the presence of potential pandemics. Entropy 22(8), no. 874 (2020); 123 pages. https://doi.org/10.3390/e22080874 | |
| M. Broniatowski, W. Stummer: Some universal insights on divergences for statistics, machine learning and artificial intelligence. In: F. Nielsen (ed.), Geometric Structures of Information, pp. 149-211. Springer, 2019. https://doi.org/10.1007/978-3-030-02520-5_8 | |
| M. Broniatowski, E. Miranda, W. Stummer: Testing the number and nature of the components in a mixture distribution. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 309–318. https://doi.org/10.1007/978-3-030-26980-7_32 | |
| B. Roensch, W. Stummer: Robust estimation by means of scaled power Bregman distances. Part I. Non-homogeneous data. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 319–330. https://doi.org/10.1007/978-3-030-26980-7_33 | |
| B. Roensch, W. Stummer: Robust estimation by means of scaled power Bregman distances. Part II. Extreme Values. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 331–340. https://doi.org/10.1007/978-3-030-26980-7_34 | |
| S. Krömer, W. Stummer: A new toolkit for mortality data analytics. In: A. Steland, E. Rafajlowicz͕, O. Okhrin (eds.), Stochastic Models, Statistics and Their Applications, Springer, 2019, pp. 393–407. https://doi.org/10.1007/978-3-030-28665-1_30 | |
| A.-L. Kißlinger, W. Stummer: A new toolkit for robust distributional change detection. Applied Stochastic Models in Business and Industry 34, pp. 682-699 (2018). https://doi.org/10.1002/asmb.2357 | |
| Cotta, V.A. Reisen, P. Bondon, W. Stummer: Robust estimation of covariance and correlation functions of a stationary multivariate process. Preprint, 2017. | |
| W. Stummer, A.-L. Kißlinger: Some new flexibilizations of Bregman divergences and their asymptotics. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2017, Lecture Notes in Computer Science 10589, Springer, 2017, pp. 514–522. https://doi.org/10.1007/978-3-319-68445-1_60 | |
| B. Roensch, W. Stummer: 3D insights to some divergences for robust statistics and machine learning. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2017, Lecture Notes in Computer Science 10589, Springer, 2017, pp. 460–469. https://doi.org/10.1007/978-3-319-68445-1_54 | |
| V.A. Reisen, C. Levy-Leduc, H.H.A. Cotta, T.T.A. Albuquerque, W. Stummer: Long-memory models under outliers: an application to air pollution level. In: B.R. Gurjar, P. Kumar, J.N. Govil (eds.), Environmental Science and Engineering, Vol. 3 – Air and Noise Pollution, Studium Press LLC, 2017, pp. 135-166. | |
| A.-L. Kißlinger and W. Stummer: Robust statistical engineering by means of scaled Bregman distances. In: C. Agostinelli, A. Basu, P. Filzmoser, D. Mukherjee (eds.), Recent Advances in Robust Statistics: Theory and Applications, Springer, 2016, pp. 81-113. https://doi.org/10.1007/978-81-322-3643-6_5 | |
| A.-L. Kißlinger and W. Stummer: New model search for nonlinear recursive models, regressions and autoregressions. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2015, Lecture Notes in Computer Science 9389, Springer, 2015, pp. 693-701. https://doi.org/10.1007/978-3-319-25040-3_74 | |
| A.-L. Kißlinger and W. Stummer: Some decision procedures based on scaled Bregman distance surfaces. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2013, Lecture Notes in Computer Science 8085, Springer, 2013, pp. 479-486. https://doi.org/10.1007/978-3-642-40020-9_52 | |
| W. Stummer and I. Vajda : On Bregman Distances and Divergences of Probability Measures. IEEE Transactions on Information Theory 58(3), pp. 1277-1288 (2012). https://doi.org/10.1109/TIT.2011.2178139 [arXiv:0911.2784] | |
| W. Stummer and W. Lao: Limits of Bayesian decision related quantities of binomial asset price models. Kybernetika 48(4), pp. 750-767 (2012). https://www.kybernetika.cz/content/2012/4/750/paper.pdf [ABSTRACT] | |
| R. Feicht and W. Stummer: An explicit non-stationary stochastic growth model. Chapter 7 of the book: O. de la Grandville (ed.), Economic Growth and Development, Frontiers of Economics and Globalization Vol. 11, 2011, pp. 141-202. Emerald Group Publishing Limited, Bingley UK. http://dx.doi.org/10.1108/S1574-8715(2011)0000011012 | |
| N.B. Kammerer and W. Stummer : Some distance bounds of branching processes and their diffusion limits. Preprint (45 pages) (2010). [arXiv:1005.3758] | |
| W. Stummer and I. Vajda: On divergences of finite measures and their applicability in statistics and information theory. Statistics 44, pp. 169-187 (2010). https://doi.org/10.1080/02331880902986919 | |
| R. Feicht and W. Stummer : Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery. IWQW Discussion Paper No. 5/2010 (29 pages) (2010). https://www.econstor.eu/bitstream/10419/41470/1/63745314X.pdf https://www.iwf.rw.fau.de/files/2016/03/05-2010.pdf | |
| W. Stummer and I. Vajda : Optimal statistical decisions about some alternative financial models. Journal of Econometrics 137, pp. 441-471 (2007). https://doi.org/10.1016/j.jeconom.2005.10.001 | |
| I. Schäl and W. Stummer : Basel-II compliant mapping of operational risks. Journal of Operational Risk 2(1), pp. 93 – 114 (2007). https://doi.org/10.21314/JOP.2007.021 | |
| W. Stummer : Some Bregman distances between financial diffusion processes. Proc. Appl. Math. Mech. 7, pp. 1050503 – 1050504 (2007). https://doi.org/10.1002/pamm.200700814 | |
| I. Schäl and W. Stummer : Kategorisierung operationeller Risiken im Umfeld von Basel II. FINANZ BETRIEB (now: CORPORATE FINANCE) 7(12), pp. 786-798 (2005). https://research.owlit.de/document/f5231ba2-a493-30aa-a96a-dd8a633a581f | |
| W. Stummer: Exponentials, Diffusions, Finance, Entropy and Information.Monograph (230 pages, ISBN 3-8322-3186-2). Shaker Verlag (2004). https://www.shaker.de/de/content/catalogue/index.asp?lang=de&ID=8&ISBN=978-3-8322-3186-6 | |
| N. Henze and W. Stummer : Means and middle values in Stochastics. (in German; original title: Mittelwerte und Mitten in der Stochastik). MU 50(5), pp. 18-29 (2004). | |
| W. Stummer : Modern Mathematical Finance for Schools. (in German; original title: Moderne Finanzmathematik für die Schule). In: R. Biehler, J. Engel and J. Meyer, eds., Neue Medien und innermathematische Vernetzungen in der Stochastik, pp. 61 — 75, Verlag Franzbecker Hildesheim/Berlin (2004). | |
| W. Stummer : Nuances of the Non-Arbitrariness of Stock Price Modelling. (in German; original title: Nuancen der Nichtbeliebigkeit von Aktienkurs-Modellierungen). Stochastik in der Schule 23(2), pp. 7-13 (2003). Typo-Corrigenda: In Definition 4.1(ii) there should be >= (greater-than-or-equal-to-symbol) instead of > (greater-than-symbol). | |
| W. Stummer : Some potential means for venture valuation. The Journal of Entrepreneurial Finance (and Business Ventures) 7(3), pp. 39-52 (2002). | |
| W. Stummer : Decision risk reductions for stock indices. Advances and Applications in Statistics 2(1), pp. 79-99 (2002). | |
| W. Stummer : Some divergence properties of asset price models. Entropy 3(5), pp. 300-324 (2001). https://doi.org/10.3390/e3050300 | |
| W. Stummer : A Toolbox for Generalized Relative Entropies, EMM and Contingent Claim Valuation. In: M. Kohlmann and S. Tang, eds., Mathematical Finance, pp. 345-354, Birkhäuser Verlag Basel (2001) | |
| W. Stummer : On a statistical information measure in a generalized Samuelson-Black-Scholes world. Statistics & Decisions (now: Statistics & Risk Modeling) 19(3), pp. 289-314 (2001). https://doi.org/10.1524/strm.2001.19.3.289 | |
| L.C.G. Rogers and W. Stummer : Consistent fitting of one-factor models to interest rate data. Insurance: Mathematics & Economics 27, pp. 45-63 (2000). https://doi.org/10.1016/S0167-6687(00)00039-1 | |
| W. Stummer : On option pricing for non-lognormal perturbations of geometric Brownian motion. ZAMM Z. Angew. Math. Mech. (Applied Mathematics and Mechanics) 80 (S3), S857-S858 (2000). | |
| W. Stummer : On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift. Statistics & Probab. Letters 46(1), pp. 43-51 (2000). https://doi.org/10.1016/S0167-7152(99)00085-1 | |
| W. Stummer and K.-Th. Sturm : On exponentials of additive functionals of Markov processes. Stochastic Processes Appl. 85, pp. 45-60 (2000). https://doi.org/10.1016/S0304-4149(99)00064-2 | |
| W. Stummer : On a statistical information measure of diffusion processes. Statistics & Decisions (now: Statistics & Risk Modeling) 17(4), pp. 359-376 (1999). https://doi.org/10.1524/strm.1999.17.4.359 | |
| W. Stummer : On arbitrage in the Black-Scholes world – a new sufficient condition. ZAMM Z. Angew. Math. Mech. (Applied Mathematics and Mechanics) 79 (S3), S925-S926 (1999). | |
| W. Stummer : On bounded entropy of solutions of multidimensional stochastic differential equations. Statistics & Probab. Letters 36(4), pp. 327-336 (1998). https://doi.org/10.1016/S0167-7152(97)00079-5 | |
| W. Stummer : On exponential moments of Brownian functionals. Statistics & Probab. Letters 31(3), pp. 233-237 (1997). https://doi.org/10.1016/S0167-7152(96)00035-1 | |
| W. Stummer : The Novikov and entropy conditions of multidimensional diffusion processes with singular drift. Probab. Theory Relat. Fields 97, pp. 515-542 (1993). https://doi.org/10.1007/BF01192962 | |
| A. Wakolbinger and W. Stummer : On Schrödinger processes and stochastic Newton equations. Institutsbericht Nr. 367, Preprint Series of the Department of Mathematics at the Johannes Kepler University Linz, 1988. | |
Lehrveranstaltungen im Wintersemester 2025/2026:
für Master Wirtschaftsmathematik und Master Mathematik:
Vorlesung „Fortgeschrittene Risikoanalyse 1“ (1. Semester, 10 ECTS)
Di, 16-18 Uhr im Hörsaal H12;
Mi, 18-20 Uhr im Hörsaal H12;Übungen: Mi, 20-21 Uhr im Hörsaal H12;
Vorlesung „Fortgeschrittene Risikoanalyse 2“ (2. Semester, 10 ECTS)
Di, 18-20 Uhr im Übungsraum 3;
Do, 16-18 Uhr im Übungsraum 3;Übungen: Di, 20-21 Uhr im Übungsraum 3;
Hauptseminar/Masterseminar „Quantitatives Risikomanagement“
(3. Semester, 5 ECTS)Do, 18-20 Uhr im Übungsraum 4;
Details: siehe https://www.campo.fau.de
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Lehrveranstaltungen im Sommersemester 2026:
für Bachelor Wirtschaftsmathematik und Bachelor Mathematik:
Bachelorseminar „Risikobewertung in den Wirtschaftswissenschaften“
(6. Semester, 5 ECTS)Do, 18-20 Uhr im Übungsraum 4;
Details: siehe https://www.campo.fau.de
———
für Master Wirtschaftsmathematik und Master Mathematik:
Vorlesung „Fortgeschrittene Risikoanalyse 2“
(2. Semester, 10 ECTS)Di, 18-20 Uhr im Hörsaal H12;
Mi, 18-20 Uhr im Hörsaal H12;Übungen: Mi, 20-21 Uhr im Hörsaal H12;