Siegelement der Uni Freiburg in Form eines Kreises

JProf. David Criens

Porträt von JProfessor  David Criens

Ich bin Juniorprofessor für Mathematische Stochastik.

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

Weitere News

Der SFB „Small Data“ mit PIs Angelika Rohde, Peter Pfaffelhuber und Thorsten Schmidt wird von der DFG mit 12 Mio EUR gefördert.

Research Interests

  • Martingale problems
  • Nonlinear stochastic processes and nonlinear semigroups
  • Diffusions
  • Stochastic (partial) differential equations

Lehre

Winterterm 2024/2025
Sommerterm 2024
Winterterm 2023/2024
Sommerterm 2023
  • Stochastik 2 (lecture)
Winterterm 2022/2023
  • Stochastik 1 (lecture) (awarded with the „teaching prize“ of the student body)
  • Nichtlineare Semimartingale und Markovprozesse (seminar)

Veröffentlichungen

Vorveröffentlichungen (Preprints)

  • No arbitrage and the existence of ACLMMs in general diffusion markets, mit Mikhail Urusov, 2024, arXiv.
  • Stochastic solutions to Hamilton-Jacobi-Bellman Dirichlet problems, 2024, arXiv.
  • Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs, mit Moritz Ritter, 2023, arXiv.
  • A stochastic representation theorem for sublinear semigroups with non-local generators, mit Lars Niemann, 2023, arXiv
  • A limit theory for controlled McKean-Vlasov SPDEs, 2023, arXiv.
  • Criteria for the absence of arbitrage in general diffusion markets, mit Mikhail Urusov, 2023, arXiv.
  • Separating times for one-dimensional diffusions, mit Mikhail Urusov, 2022, arXiv.

Veröffentlichungen 

Zur Veröffentlichung akzeptiert

  • Nonlinear semimartingales and Markov processes with jumps, mit Lars Niemann, to appear in Journal of Evolution EquationsarXiv.
  • Robust market convergence: from discrete to continuous time, to appear in SIAM Journal on Financial Mathematics, arXiv.
  • On the representation property for 1D general diffusion semimartingales, mit Mikhail Urusov, to appear in Theory of Probability and its ApplicationsarXiv.
2024 
  • A convergence theorem for Crandall-Lions viscosity solutions to path-dependent Hamilton-Jacobi-Bellman PDEs, Nonlinear Differential Equations and Applications NoDEA, 31:97, 2024, article.
  • Markov selections and Feller properties of nonlinear diffusions, mit Lars NiemannStochastic Processes and their Applications, 173:104354, 2024, article.
  • Stochastic processes under parameter uncertainty, Journal of Mathematical Analysis and Applications, 538:(2), 128388, 2024, article.
  • A class of multidimensional nonlinear diffusions with the Feller property, mit Lars NiemannStatistics and Probability Letters, 208:1100572024, article.
2023
  • Nonlinear continuous semimartingales, mit Lars NiemannElectronic Journal of Probability, 28(146), 1-40, 2023, article.
  • On the relation of one-dimensional diffusions on natural scale and their speed measures, Journal of Theoretical Probability, 36(4), 2339-2358, 2023, article.
  • Robust utility maximization with nonlinear continuous semimartingales, mit Lars Niemann, Mathematics and Financial Economics, 17, 499-536, 2023, article.
  • Propagation of chaos for weakly interacting mild solutions to stochastic partial differential equations, Journal of Statistical Physics, 190:114, 2023, article.
  • On the Feller-Dynkin and the martingale property of one-dimensional diffusions, Electronic Communications in Probability, 28(20), 1-15, 2023, article.
  • The martingale problem method revisited, mit Peter Pfaffelhuber und Thorsten SchmidtElectronic Journal of Probability, 28(19), 1-46, 2023, article.
2022
  • On a theorem by A.S. Cherny for semilinear stochastic partial differential equations, mit Moritz RitterJournal of Theoretical Probability, 35, 2052-2067, 2022, article.
  • A parabolic Harnack principle for balanced difference equations in random environment, mit Noam BergerArchive for Rational Mechanics and Analysis, 245(2), 899-947, 2022, article.
2021
  • 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.
2020
  • 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
2019
  • 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.
2018
  • Absolute continuity of semimartinges, mit 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.
2017
  • Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models, mit Kathrin Glau und Zorana GrbacApplied Mathematical Finance, 24(1), 23-37, 2017, article.

Doktorarbeit

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