I am a postdoctoral researcher at the Humboldt University of Berlin in the team of Ulrich Horst in the Applied Financial Mathematics & Applied Stochastic Analysis research group.

Previously, I was a scientific assistant in a Math+ Project at TU Berlin and a PhD student under the supervision of Peter K. Friz and Christian Bayer.

In the spring semester 2022 I am teaching the course Continuous Time Finance.

Short CV

since October 2021 Postdoctoral Researcher at Humboldt Universität zu Berlin
September 2021 Dr. rer. nat., Technische Universität Berlin
April 2019 - September 2021 Scientific Assistant at Technische Universität Berlin
March 2019 Master of Science, Technische Universität Berlin

You can find my detailed CV here: PDF.​​​​​​

Research Interest

  • Signatures and their applications in stochastic optimization and machine learning.
  • Fractional Brownian motion, log-correlated fields, Gaussian multiplicative chaos and their applications to volatility modelling.


  • C. Bayer, P. Hager, S. Riedel, J. Schoenmakers, Optimal stopping with signatures, 03 May 2021, arXiv (accepted at the Annals of Applied Probability)
  • P. K. Friz, P. Hager, N. Tapia, Unified Signature Cumulants and Generalized Magnus Expansions, 8 Feb 2021, arxiv (accepted at the Forum of Mathematics, Sigma)
  • C. Bayer, D. Belomestny, P. Hager, P. Pigato, J. Schoenmakers, V. Spokoiny, Reinforced optimal control, 24 Nov 2020, arxiv (accepted in the Communications in Mathematical Sciences)
  • P. Hager, E. Neuman, The Multiplicative Chaos of H=0 Fractional Brownian Fields, 4 Aug 2020, arxiv (accepted at the Annals of Applied Probability)


  • C. Bayer, D. Belomestny, P. Hager, P. Pigato, J. Schoenmakers, Randomized optimal stopping algorithms and their convergence analysis, SIAM Journal on Financial Mathematics, 12(3), 1201–1225 (2021), (journalarxiv)



Paul Hager
Humboldt University Berlin
Department of Mathematics
Unter den Linden 6
10099 Berlin

Rudower Chaussee 25
Haus 1; Suite 105
12486 Berlin

+49 (0) 30 2093 45403

Email address: