# Dr. Stefan Tappe

Academic Staff

This position is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Module "Temporary Positions for Principal Investigators".

## Address:** **

Department of Mathematical Stochastics

Albert Ludwig University of Freiburg

Ernst-Zermelo-Straße 1

Room 111

79104 Freiburg (Germany)

Phone: +49-761-203-7708

Fax: +49-761-203-5661

E-Mail: stefan.tappe@math.uni-freiburg.de

## Research Interests

- Stochastic Analysis
- Stochastic Partial Differential Equations
- Financial Mathematics

## Publications

**Current Preprints**

- Tappe, S. (2024): Invariant submanifolds for solutions to rough differential equations. 15 pages (arXiv)
- Tappe, S. (2024): Mild solutions to semilinear rough partial differential equations. 49 pages (arXiv)
- Tappe, S. (2023): Invariant cones for jump-diffusions in infinite dimensions. 46 pages (arXiv)
- Bhaskaran, R., Tappe, S. (2023): A note on invariant manifolds for stochastic partial differential equations in the framework of the variational approach. 10 pages (arXiv)
- Tappe, S. (2023): Linear estimators for Gaussian random variables in Hilbert spaces. 17 pages (arXiv)
- Nakayama, T., Tappe, S. (2022): Distance between closed sets and the solutions to stochastic partial differential equations. 34 pages (arXiv)

#### Publications in International Journals

- Bhaskaran, R., Tappe, S. (2024): Stochastic partial differential equations and invariant manifolds in embedded Hilbert spaces. Accepted for publication in
*Potential Analysis*(arXiv) - Platen, E., Tappe, S. (2023): No arbitrage and multiplicative special semimartingales.
*Advances in Applied Probability***55**(3), 1033-1074 - Platen, E., Tappe, S. (2023): Exploiting arbitrage requires short selling.
*Frontiers of Mathematical Finance***2**(3), 265-282 (arXiv) - Tappe, S. (2022): An addendum to "Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients".
*Theory of Probability and Mathematical Statistics***107**, 173-184 (arXiv) - Tappe, S. (2021): The dual Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations.
*Theory of Probability and Mathematical Statistics***105**, 51-68 (arXiv) - Tappe, S. (2021): Permutation invariant strong law of large numbers for exchangeable sequences. Journal of Probability and Statistics,
**vol. 2021**, Article ID 3637837, 5 pages (arXiv) - Platen, E., Tappe, S. (2021): No-arbitrage concepts in topological vector lattices.
*Positivity***25**(5), 1853-1898 (arXiv) - Tappe, S. (2021): Mild solutions to semilinear stochastic partial differential equations with locally monotone coefficients.
*Theory of Probability and Mathematical Statistics***104**, 113-122 (arXiv) - Tappe, S. (2021): A note on the von Weizsäcker theorem.
*Statistics and Probability Letters***168**, Article 108926, 6 pages (arXiv) - Schmidt, T., Tappe, S., Yu, W. (2020): Infinite dimensional affine processes.
*Stochastic Processes and Their Applications***130**(12), 7131-7169 (arXiv) - Nakayama, T., Tappe, S. (2018): Wong-Zakai approximations with convergence rate for stochastic partial differential equations.
*Stochastic Analysis and Applications***36**(5), 832-857 (arXiv) - Tappe, S. (2017): Invariance of closed convex cones for stochastic partial differential equations.
*Journal of Mathematical Analysis and Applications***451**(2), 1077-1122 (arXiv) - Tappe, S. (2016): Affine realizations with affine state processes for stochastic partial differential equations.
*Stochastic Processes and Their Applications***126**(7), 2062-2091 (arXiv) - Tappe, S. (2015): Flatness of invariant manifolds for stochastic partial differential equations driven by Lévy processes.
*Electronic Communications in Probability***20**(40), 1-11 (arXiv) - Tappe, S. (2015): Existence of affine realizations for stochastic partial differential equations driven by Lévy processes.
*Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences***471**(2178) (arXiv) - Platen, E., Tappe, S. (2015): Real-world forward rate dynamics with affine realizations.
*Stochastic Analysis and Applications***33**(4), 573-608 (arXiv) - Filipović, D., Tappe, S., Teichmann, J. (2014): Invariant manifolds with boundary for jump-diffusions.
*Electronic Journal of Probability***19**(51), 1-28 (arXiv) - Küchler, U., Tappe, S. (2014): Exponential stock models driven by tempered stable processes.
*Journal of Econometrics***181**(1), 53-63 (arXiv) - Tappe, S., Weber, S. (2014): Stochastic mortality models: An infinite dimensional approach.
*Finance and Stochastics***18**(1), 209-248 (arXiv) - Tappe, S. (2013): Compact embeddings for spaces of forward rate curves.
*Abstract and Applied Analysis*, vol.**2013**, Article ID 709505, 6 pages (arXiv) - Küchler, U., Tappe, S. (2013): Tempered stable distributions and processes.
*Stochastic Processes and Their Applications***123**(12), 4256-4293 (arXiv) - Tappe, S. (2013): Foundations of the theory of semilinear stochastic partial differential equations.
*International Journal of Stochastic Analysis*, vol.**2013**, Article ID 798549, 25 pages (arXiv) - Tappe, S. (2013): The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations.
*Electronic Communications in Probability***18**(24), 1-13 (arXiv) - Tappe, S. (2013): The Itô integral with respect to an infinite dimensional Lévy process: A series approach.
*International Journal of Stochastic Analysis*, vol.**2013**, Article ID 703769, 14 pages (arXiv) - Tappe, S. (2012): Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures.
*International Journal of Stochastic Analysis*, vol.**2012**, Article ID 236327, 24 pages (arXiv) - Tappe, S. (2012): Existence of affine realizations for Lévy term structure models.
*Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences***468**(2147), 3685-3704 (arXiv) - Rüdiger, B., Tappe, S. (2012): Isomorphisms for spaces of predictable processes and an extension of the Itô integral.
*Stochastic Analysis and Applications***30**(3), 529-537 (arXiv) - Filipović, D., Tappe, S., Teichmann, J. (2010): Jump-diffusions in Hilbert spaces: Existence, stability and numerics.
*Stochastics***82**(5), 475-520 (arXiv) - Filipović, D., Tappe, S., Teichmann, J. (2010): Term structure models driven by Wiener processes and Poisson measures: Existence and positivity.
*SIAM Journal on Financial Mathematics***1**(1), 523-554 (arXiv) - Tappe, S. (2010): An alternative approach on the existence of affine realizations for HJM term structure models.
*Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences***466**(2122), 3033-3060 (arXiv) - Tappe, S. (2010): A note on stochastic integrals as L^2-curves.
*Statistics and Probability Letters***80**(13-14), 1141-1145 (arXiv) - Küchler, U., Tappe, S. (2009): Option pricing in bilateral Gamma stock models.
*Statistics and Decisions***27**(4), 281-307 (arXiv) - Küchler, U., Tappe, S. (2008): On the shapes of bilateral Gamma densities.
*Statistics and Probability Letters***78**(15), 2478-2484 (arXiv) - Filipović, D., Tappe, S. (2008): Existence of Lévy term structure models.
*Finance and Stochastics***12**(1), 83-115 (arXiv) - Küchler, U., Tappe, S. (2008): Bilateral Gamma distributions and processes in financial mathematics.
*Stochastic Processes and Their Applications***118**(2), 261-283 (arXiv)

#### Publications in Refereed Conference Proceedings

- Schmidt, T., Tappe, S. (2015): Dynamic term structure modelling with default and mortality risk: New results on existence and monotonicity.
*Banach Center Publications***105**(2015), 211-238 (arXiv) - Mandrekar, V., Rüdiger, B., Tappe, S. (2013): Itô's formula for Banach space valued jump processes driven by Poisson random measures.
*Seminar on Stochastic Analysis, Random Fields and Applications VII*, Progress in Probability**67**, Birkhäuser Verlag, 171-186

#### Articles of general interest

- Tappe, S. (2020): A simple mathematical model for the evolution of the corona virus. 6 pages (arXiv)

#### Further Articles

- Bhaskaran, R., Tappe, S. (2022): Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces. 74 pages. Electronic appendix of the article "Stochastic partial differential equations and invariant manifolds in embedded Hilbert spaces" (arXiv)
- Filipović, D., Tappe, S., Teichmann, J. (2014): Stochastic partial differential equations and submanifolds in Hilbert spaces. Electronic appendix of the article "Invariant manifolds with boundary for jump-diffusions" (arXiv)

#### Textbooks

- Tappe, S. (2023): Stochastische partielle Differentialgleichungen. (Stochastic Partial Differential Equations.) Springer-Verlag GmbH, 57 pages
- Tappe, S. (2013): Einführung in die Wahrscheinlichkeitstheorie. (Introduction to Probability Theory.) Springer-Verlag Berlin Heidelberg, 303 pages

#### Theses

- Tappe, S. (2005):
*Finite dimensional realizations for term structure models driven by semimartingales.*PhD Thesis, Humboldt University of Berlin, 153 pages (edoc-Server) - Tappe, S. (2002):
*Cellular resolutions of monomial ideals.*Diploma Thesis, University of Paderborn, 171 pages

## Organized Conferences

- International Conference Recent Developments in the Mathematics of Machine Learning at the University of Wuppertal, scheduled for 26 March 2024.
- International Online Workshop Stochastic Analysis and Hermite Sobolev Spaces, organized together with Rajeev Bhaskaran (Indian Statistical Institute, Bangalore Centre, India) and Suprio Bhar (Indian Institute of Technology Kanpur, India), 21-26 June 2021

## Teaching

#### Summer 2024 (University of Wuppertal)

- Actuarial Mathematics (Lecture, 4 hours per week)
- Risk Theory (Lecture, 4 hours per week)

#### Winter 2023/24 (University of Wuppertal)

- Introduction to Stochastics (Lecture and Exercise Class, 4+2 hours per week)
- Statistical and Machine Learning (Seminar, 2 hours per week)

#### Summer 2023 (University of Wuppertal)

- Applied Statistics (Lecture and Exercise Class, 4+2 hours per week)
- Risk Theory (Lecture and Exercise Class, 2+1 hours per week)

#### Winter 2022/23 (University of Rostock)

- Stochastics for Bachelors (Lecture, 4 hours per week)
- Introduction to Actuarial and Financial Mathematics (Lecture, 4 hours per week)

#### Winter 2020/21 (Karlsruhe Institute of Technology)

- Stochastic Differential Equations (Lecture and Exercise Class, 4+2 hours per week)
- Statistical and Machine Learning (Seminar, jointly with Prof. Dr. Daniel Hug, 2+1 hours per week)

#### Summer 2020 (Karlsruhe Institute of Technology)

- Actuarial Mathematics (Lecture and Exercise Class, 4+2 hours per week)
- Topology (Seminar, 2+1 hours per week)

#### Winter 2019/20 (Ludwig Maximilian University of Munich)

- Financial Mathematics in discrete time (Lecture, 4 hours per week)
- Nonlinear Expectations (Seminar, 2 hours per week)

#### Summer 2019 (Albert Ludwig University of Freiburg)

- Risk Theory (Lecture and Exercise Class, 2+1 hours per week)

#### Winter 2018/19 (Albert Ludwig University of Freiburg)

- Mathematical Statistics (Lecture and Exercise Class, 4+2 hours per week)
- Actuarial Mathematics (Lecture and Exercise Class, 2+2 hours per week)

#### Summer 2018 (Albert Ludwig University of Freiburg)

- Markov Chains (Lecture and Exercise Class, 2+2 hours per week)
- Stochastic Integration and Financial Mathematics (Exercise Class, 2 hours per week)

#### Winter 2017/18 (Albert Ludwig University of Freiburg)

- Stochastic Processes (Lecture and Exercise Class, 4+2 hours per week)
- Stochastic Analysis with Rough Paths (Lecture and Exercise Class, 2+2 hours per week)

#### Winter 2016/17 (University of Hannover)

- Financial Mathematics in continuous time (Lecture, 4 hours per week)

#### Summer 2016 (University of Hannover)

- Stochastic Analysis (Lecture, 4 hours per week)

#### Winter 2015/16 (University of Hannover)

- Affine Processes (Lecture, 4 hours per week)

#### Summer 2015 (University of Hannover)

- Stochastic Analysis (Lecture, 4 hours per week)

#### Winter 2014/15 (University of Hannover)

- Stochastics A (Service-Lecture, 2 hours per week)
- Stochastic Analysis (Seminar, 2 hours per week)

#### Summer 2014 (University of Hannover)

- Stochastic Analysis (Lecture, 4 hours per week)

#### Winter 2013/14 (University of Hannover)

- Stochastics II (Lecture, 4 hours per week)

#### Summer 2013 (University of Hannover)

- Stochastics I (Lecture, 4 hours per week)

#### Winter 2012/13 (University of Hannover)

- Stochastics II (Lecture, 4 hours per week)

#### Summer 2012 (University of Hannover)

- Stochastics I (Lecture, 4 hours per week)

#### Winter 2011/12 (University of Hannover)

- Recent Developments in Financial Mathematics (Lecture, 4 hours per week)

#### Summer 2011 (University of Hannover)

- Stochastic Analysis (Lecture, 4 hours per week)

#### Winter 2010/11 (ETH Zurich)

- Interest Rate Theory (Exercise Class, 2 hours per week and coordination of duties)

#### Summer 2009 (Vienna University of Technology)

- Stochastic Analysis (Lecture and Exercise Class, 3+1 hours per week)

#### Winter 2008/09 (Vienna University of Technology)

- Stochastic Analysis in Finance and Insurance (Exercise Class, 1 hour per week)

#### Summer 2007 (Ludwig Maximilian University of Munich)

- Analysis II (Exercise Class, 4 hours per week and coordination of duties)

#### Winter 2006/07 (Ludwig Maximilian University of Munich)

- Analysis I (Exercise Class, 4 hours per week and coordination of duties)

#### Summer 2006 (Ludwig Maximilian University of Munich)

- Analysis III (Exercise Class, 4 hours per week and coordination of duties)

#### Winter 2005/06 (Ludwig Maximilian University of Munich)

- Analysis II (Exercise Class, 4 hours per week and coordination of duties)

## Advised Theses

#### Karlsruhe Institute of Technology

*Johannes Schuler*(Master Thesis): Mathematical Modeling of Pandemics with Differential Equations. August 2021 to March 2022 (External supervisor)*Sebastian Gottheil*(Bachelor Thesis): Credibility Theory. October 2020 to February 2021*Christian Saulich*(Bachelor Thesis): Reservation for delayed claims. September 2020 to March 2021

#### Ludwig Maximilian University of Munich

*Pavel Kartsovnik*(Bachelor Thesis): Nonlinear expectations and risk measures. December 2019 to January 2020*Doriane Audrey Nkeng Mbetntang*(Master Thesis): Premium principles and experience rating. October 2019 to April 2020

#### Albert Ludwig University of Freiburg

*Lena Burkhardt*(Bachelor Thesis): The Pólya urn model and its passage times. May 2019 to July 2019*Roman Haak*(Masterarbeit): Algebraic structures of stochastic integrals and their applications. October 2018 to March 2019*Lorenz Denk*(Bachelor Thesis): Parameter estimation and pricing in discrete-time financial models. May 2018 to August 2018*Anna Maddux*(Bachelor Thesis): Symmetric random walks and a generalization of the Borel-Cantelli lemma. April 2018 to July 2018*Hang Zhou*(Masterarbeit): Vector-valued stochastic integration and applications to financial mathematics. January 2018 to July 2018

#### University of Hannover

*Tahirivonizaka Rahantamialisoa*(PhD Thesis): A unified approach to SPDEs driven by semimartingale fields. April 2012 to February 2017; the defence took place at March 15th, 2017*Apostolos Sideris*(Master Thesis): Affine processes on symmetric cones. July 2016 to January 2017*Pascal Schoppe*(Master Thesis): Pathwise uniqueness of the solutions to stochastic partial differential equations. April 2016 to October 2016*Kwok-Yin Choi*(Master Thesis): No-Arbitrage concepts in financial market models. February 2016 to August 2016*Waldemar Schäfer*(Bachelor Thesis): Characterizations and extensions of Panjer's class. July 2015 to October 2015*Gabriele Carulli*(Master Thesis): Functionals of affine processes with applications to finance. May 2015 to November 2015*Sarah Martens*(Master Thesis): The Skorokhod embedding problem. January 2015 to July 2015*Michael Fiedler*(Master Thesis): Markov semigroups and stochastic processes in infinite dimension. October 2014 to April 2015*Johanna Schmidt*(Master Thesis): A trajectorial interpretation of Doob's martingale inequalities. September 2014 to March 2015*Harald Klingebiel*(Bachelor Thesis): Convergence rates for the Berry-Esseen inequality. August 2014 to October 2014*Pascal Schoppe*(Bachelor Thesis): Deterministic and stochastic evolution equations. May 2014 to August 2014*André Löper*(Bachelor Thesis): Panjer distributions. May 2014 to July 2014*Sören Schwark*(Bachelor Thesis): Regression analysis of the linear dependence of financial data. April 2014 to June 2014*Tim Massel*(Bachelor Thesis): Coupling and uniform ergodicity of discrete Markov chains. April 2014 to July 2014*Martin Sanojca*(Bachelor Thesis): Bonferroni inequalities. February 2014 to May 2014*Apostolos Sideris*(Bachelor Thesis): Characteristic functions and infinitely divisible distributions. November 2013 to February 2014*Henry Wegener*(Master Thesis): Almost everywhere convergence of sequences of operators and its connection to modern and classical ergodic theory. November 2013 to May 2014*Maria Óskarsdóttir*(Master Thesis): On the uniqueness of solutions to stochastic differential equations. October 2013 to April 2014*Gabriele Carulli*(Bachelor Thesis): Option pricing in exponential L\'evy models. October 2013 to November 2013*Sarah Klünder*(Bachelor Thesis): Bivariate exponential distributions. October 2013 to December 2013*Johanna Schirmer*(Bachelor Thesis): Markov chains with finite state space. October 2013 to December 2013*Nikolas Nüsken*(Master Thesis): The stochastic wave equation. August 2013 to February 2014*Tina Kolodinski*(Bachelor Thesis): Geometric characterizations of arbitrage free financial models. July 2013 to September 2013*Patrick Kiedrowski*(Bachelor Thesis): Laws of large numbers. May 2013 to July 2013*Florian Modler*(Master Thesis): Invariant manifolds and foliations for stochastic partial differential equations and random dynamical systems. June 2012 to September 2012*Dirk Skowasch (Diploma Thesis)*: Lévy processes in financial mathematics. May 2012 to November 2012

#### Vienna University of Technology

*Piet Porkert*(Diploma Thesis): On weak solutions to SDEs in Hilbert spaces. August 2010 to February 2011

#### Ludwig Maximilian University of Munich

*Yong Shang*(Diploma Student of Damir Filipović): Heath-Jarrow-Morton model with square root volatility. August 2007 to February 2008

Seven of my Master Students obtained offers for PhD positions; namely:

- Apostolos Sideris (Dresden University of Technology, Germany)
- Pascal Schoppe (University of Augsburg and Dresden University of Technology, Germany)
- Michael Fiedler (University of Duisburg-Essen, University of Hildesheim and University of Paderborn, Germany)
- Henry Wegener (Albert Einstein Institute Hannover and Martin Luther University of Halle-Wittenberg, Germany)
- Maria Óskarsdóttir (University of Leuven, Belgium)
- Nikolas Nüsken (Imperial College London, United Kingdom)
- Piet Porkert (Vienna University of Technology, Austria)

## Curriculum Vitae

#### Education

*Achievements being equivalent to Habilitation:*Successful Mid-Term Evaluation of my Junior Professorship, University of Hannover, March 2014*PhD in Mathematics*, Humboldt University of Berlin, November 2005*Diploma in Mathematics*, University of Paderborn, August 2002

#### Awards and Fellowships

*Award for Excellent Achievements in Mathematics*("Preis der Fakultät 2002"), University of Paderborn, February 2003*DFG Research Fellowship*(DFG-Graduiertenkolleg 251 "Stochastische Prozesse und probabilistische Analysis"), Oktober 2002 bis September 2005

#### Employment and Academic Positions

(W2-Professorship), University of Wuppertal, since April 2023*Deputy Professor**Deputy Professor*(W3-Professorship), University of Rostock, October 2022 to March 2023*Research Position*funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, since April 2021 (Currently interrupted due to the aforementioned Deputy Professorships.)*Deputy Professor*(W3-Professorship), Institute of Stochastics, Karlsruhe Institute of Technology, April 2020 to March 2021*Deputy Professor*(W3-Professorship), Department of Mathematics, Ludwig Maximilian University of Munich, October 2019 to March 2020*Academic Staff*(Deputy of a Junior Professorship), Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, April 2019 to July 2019*Deputy Professor*(W3-Professorship), Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, October 2018 to March 2019*Academic Staff*, Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, April 2018 to September 2018*Deputy Professor*(W3-Professorship), Department of Mathematical Stochastics, Albert Ludwig University of Freiburg, October 2017 to March 2018*Academic Guest*, Bernoulli Center, EPF Lausanne, Switzerland, April 2017 to June 2017*Junior Professor*, Institute of Probability and Statistics, University of Hannover, April 2011 to March 2017; this position has been extended in April 2014 after a successful mid-term evaluation for further three years*Postdoc*in the group of Josef Teichmann, Department of Mathematics, ETH Zurich, Switzerland, October 2009 to March 2011*Senior Scientist*in the group of Damir Filipović, Vienna Institute of Finance, University of Vienna and Vienna University of Economics and Business, Austria, October 2007 to September 2009*Research and Teaching Assistant*in the group of Damir Filipović, Department of Mathematics, Ludwig Maximilian University of Munich, October 2005 to September 2007*Research Fellow*in the group of Uwe Küchler, Department of Mathematics, Humboldt University of Berlin, October 2002 to September 2005*Student Assistant*, Department of Mathematics and Computer Sciences, University of Paderborn, April 1999 to July 2002