Paul Hager

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

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.

​Preprints

• C. Bayer, P. Hager, S. Riedel, J. Schoenmakers, Optimal stopping with signatures, 03 May 2021, arXiv (accepted at the Annals of Applied Probability)
• 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)

Publications

• P. K. Friz, P. P. Hager, N. Tapia, Unified Signature Cumulants and Generalized Magnus Expansions, Forum of Mathematics, Sigma, 10, E42. (2022), (journal, arxiv)
•  P. Hager, E. Neuman, The multiplicative chaos of H = 0 fractional Brownian fields., Annals of Applied Probability, 32 (3) 2139 - 2179 June 2022, (journal, arxiv)
• 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), (journal, arxiv)

Selected Talks

• Mini-Course on Machine Learning Methods in Finance @ KAUST
  • Lecture on Calculation of Deep Log Signature Stopping Rules, 23 May 2022, [html], [youtube]
  • Exercise Sheet on the Simulation of fractional Brownian motion [pdf]
• Unified Signature Cumulants and Generalized Magnus Expansions, 24 Feb 2021, Cumulants in Stochastic Analysis, (slides), (video)