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JProf. Dr. David Criens

I am Juniorprofessor for Mathematical Stochastics at the University of Freiburg. 

Personal Homepage: https://sites.google.com/view/david-criens

 

Office hour (Sprechstunde)

Nach Vereinbarung per Email

 

Adresse

Abteilung für Mathematische Stochastik  
Albert-Ludwigs-Universität Freiburg  
Ernst-Zermelo-Straße 1  
79104 Freiburg i. Br. (Germany)  

Raum: 223
Telefon: +49 - 761 - 203 - 5670
Fax: +49 - 761 - 203 - 5661 
E-Mail: david[dot]criens[at]stochastik[dot]uni-freiburg[dot]de

 

 

Research Interests

 

  • Martingale problems
  • Nonlinear stochastic processes and nonlinear semigroups
  • Diffusions
  • Stochastic (partial) differential equations
  • Random walks in random environment

 

Preprints

 

  • Stochastic processes under parameter uncertainty, 2022, arXiv.
  • Robust utility maximization with nonlinear continuous semimartingales, with Lars Niemann, 2022, arXiv.
  • A class of multidimensional nonlinear diffusions with the Feller property, with Lars Niemann, 2022, arXiv
  • Markov selections and Feller properties of nonlinear diffusions, with Lars Niemann, 2022, arXiv
  • Nonlinear continuous semimartingales, with Lars Niemann, 2022, arXiv.
  • On the relation of one-dimensional diffusions on natural scale and their speed measures, 2021, arXiv.
  • The martingale problem method revisited, with Peter Pfaffelhuber and Thorsten Schmidt, 2021, arXiv.
  • Propagation of chaos for weakly interacting mild solutions to stochastic partial differential equations, 2021, arXiv.
  • On the Feller-Dynkin and the martingale property of one-dimensional diffusions, 2021, arXiv.

  

Accepted for Publication

 

  • On a theorem by A.S. Cherny for semilinear stochastic partial differential equations, with Moritz RitterJournal of Theoretical Probability, article, online first.

 

Publications

 

  • A parabolic Harnack principle for balanced difference equations in random environment, with Noam BergerArchive for Rational Mechanics and Analysis, 245(2), 899-947, 2022, article.
  • A dual Yamada-Watanabe theorem for Levy driven stochastic differential equations, Electronic Communications in Probability, 26(18), 1-10, 2021, article.
  • On absolute continuity and singularity of multidimensional diffusions, Electronic Journal of Probability, 26(12), 1-26, 2021, article.
  • Lyapunov criteria for the Feller-Dynkin property of martingale problems, Stochastic Processes and their Applications, 130(5), 2693-2736, 2020, article.
  • No arbitrage in continuous financial markets, Mathematics and Financial Economics, 14, 461-506, 2020, article.
  • A note on real-world and risk-neutral dynamics for Heath-Jarrow-Morton frameworks, International Journal of Theoretical and Applied Finance, 23(3), 2050020, 2020, article.
  • On the existence of semimartingales with continuous characteristics, Stochastics, 92(5), 785-813, 2020, article.
  • Correction to: Cylindrical martingale problems associated with Levy generators, Journal of Theoretical Probability, 33, 1791-1800, 2020, article.
  • Limit theorem for cylindrical martingale problems associated with Levy generators, Journal of Theoretical Probability, 33, 866-905, 2020, article
  • Cylindrical martingale problems associated with Levy generators, Journal of Theoretical Probability, 32, 1306-1359, 2019, articlecorrection.
  • Couplings for processes with independent increments, Statistics and Probability Letters, 146, 161-167, 2019, article.
  • Absolute continuity of semimartinges, with Kathrin GlauElectronic Journal of Probability, 23(125), 1-28, 2018, article.
  • A note on the monotone stochastic order for processes with independent increments, Statistics and Probability Letters, 135, 127-131, 2018, article.
  • Structure preserving equivalent martingale measures for H-SII models, Journal of Applied Probability, 55(1), 1-14, 2018, article.
  • Deterministic criteria for the absence and existence of arbitrage in multi-dimensional diffusion markets, International Journal of Theoretical and Applied Finance, 21(1), 1850002, 2018, article.
  • Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models, with Kathrin Glau and Zorana GrbacApplied Mathematical Finance, 24(1), 23-37, 2017, article.

 

Ph.D. Thesis

 

Essays on Stochastic Processes and their Applications, 2020, Technical University of Munich, supervised by Noam Berger.

 

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