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Preprints

• David Criens: Stochastic solutions to Hamilton-Jacobi-Bellman Dirichlet problems, 2024, submitted, arXiv.

• David Criens: Robust market approximations: from discrete to continuous time, 2024, submitted, arXiv.

• David Criens and Moritz Ritter: Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs, 2023, submitted, arXiv.

• David Criens and Lars Niemann: A stochastic representation theorem for sublinear semigroups with non-local generators, 2023, submitted, arXiv.

• David Criens and Lars Niemann: Nonlinear semimartingales and Markov processes with jumps, 2023, submitted, arXiv.

• David Criens: A limit theory for controlled McKean-Vlasov SPDEs, 2023, submitted, arXiv.

• David Criens and Mikhail Urusov: Criteria for NUPBR, NFLVR and the existence of EMMs in integrated diffusion markets, 2023, submitted, arXiv.

• David Criens and Mikhail Urusov: Separating times for one-dimensional diffusions, 2022, submitted, arXiv.

Publications

Accepted for Publication

• David Criens and Mikhail Urusov: On the representation property for 1D general diffusion semimartingales, to appear in Theory of Probability and its Applications, arXiv.

• David Criens: A convergence theorem for Crandall-Lions viscosity solutions to path-dependent Hamilton-Jacobi-Bellman PDEs, to appear in Nonlinear Differential Equations and Applications NoDEA, arXiv.

2024

• David Criens and Lars Niemann: Markov selections and Feller properties of nonlinear diffusions, Stochastic Processes and their Applications, 173:104354.

• David Criens: Stochastic processes under parameter uncertainty, Journal of Mathematical Analysis and Applications, 538(2):128388.

• David Criens and Lars Niemann: A class of multidimensional nonlinear diffusions with the Feller property, Statistics and Probability Letters, 208:110057.

2023

• David Criens and Lars Niemann: Nonlinear continuous semimartingales, Electronic Journal of Probability, 28(146), 1-40.  

• David Criens: On the relation of one-dimensional diffusions on natural scale and their speed measures, Journal of Theoretical Probability, 36(4), 2339-2358.

• David Criens and Lars Niemann: Robust utility maximization with nonlinear semimartingales, Mathematics and Financial Economics, 17, 499-536.

• David Criens: Propagation of chaos for weakly interacting mild solutions to stochastic partial differential equations, Journal of Statistical Physics, 190:114.

• David Criens: On the Feller-Dynkin and the martingale property of one-dimensional diffusions, Electronic Communications in Probability, 28(20), 1-15.

• David Criens, Peter Pfaffelhuber and Thorsten Schmidt: The martingale problem method revisisted, Electronic Journal of Probability, 28(19), 1-46.

2022

• David Criens and Moritz Ritter: On a theorem by A.S. Cherny for semilinear stochastic partial differential equations, Journal of Theoretical Probability, 35, 2052-2067.

• Noam Berger and David Criens: A parabolic Harnack principle for balanced difference equations in random environments, Archive for Rational Mechanics and Analysis,  245, 899-947. 

2021

• David Criens: A dual Yamada-Watanabe theorem for Levy driven stochastic differential equations, Electronic Communications in Probability, 26(18), 1-10.

• David Criens: On Absolute Continuity and Singularity of Multidimensional Diffusions, Electronic Journal of Probability, 26(12), 1-26.

2020

• David Criens: Lyapunov Criteria for the Feller-Dynkin Property of Martingale Problems, Stochastic Processes and their Applications, 130(5), 2693-2736.

• David Criens: Limit Theorems for Cylindrical Martingale Problems associated with Levy Generators, Journal of Theoretical Probability, 33, 866-905.

• David Criens: No Abitrage in Continuous Financial Markets, Mathematics and Financial Economics, 14, 461-506.

• David Criens: A Note on Real-World and Risk-Neutral Dynamics for Heath-Jarrow-Morton Frameworks, International Journal of Theoretical and Applied Finance (IJTAF), 23(3), 2050020.

• David Criens: Correction to: Cylindrical Martingale Problems Associated with Lévy Generators, Journal of Theoretical Probability, 33, 1791-1800.

• David Criens: On the Existence of Semimartingales with Continuous Characteristics, Stochastics, 92(5), 785-813.

2019

• David Criens: Cylindrical Martingale Problems Associated with Lévy Generators, Journal of Theoretical Probability, 32, 1306-1359. [Correction]

• David Criens: Couplings for Processes with Independent Increments, Statistics and Probability Letters, 146, 161-167.

2018

• David Criens and Kathrin Glau: Absolute Continuity of Semimartingales, Electronic Journal of Probability, 23(125), 1-28.

• David Criens: A Note on the Monotone Stochastic Order for Processes with Independent Increments, Statistics and Probability Letters, 135, 127-131.

• David Criens: Structure Preserving Equivalent Martingale Measures for H-SII Models, Journal of Applied Probability, 55(1), 1-14.

• David Criens: Deterministic Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets, International Journal of Theoretical and Applied Finance (IJTAF), 21(1),1850002.

2017

• David Criens, Kathrin Glau and Zorana Grbac: Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models, Applied Mathematical Finance, 24(1), 23-37.

Ph.D. Thesis

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

My Erdös number is 3.