Ibrahim Ekren

Associate Professor of Mathematics

University of Michigan 

Department of Mathematics 

530 Church St, Ann Arbor, MI 48109

Office: 2856 East Hall

Email: iekren@umich.edu

Bio :

Since 2023, I have been an Associate Professor in the Department of Mathematics at the University of Michigan. Here is my CV (updated 2024) and you may find my google scholar page here.

From 2018 to 2023, I served as an Assistant Professor in the Department of Mathematics at Florida State University. Prior to that, I was a Byrne Postdoctoral Assistant Professor in the Department of Mathematics at the University of Michigan from 2017 to 2018. From 2014 to 2017, I held a postdoctoral research position in the Department of Mathematics at ETH Zurich.

Between 2010 and 2014, I pursued my Ph.D. in Mathematics at the University of Southern California, under the supervision of Professor Jianfeng Zhang. In 2010, I earned both my master’s degree in Mathematics from Université Pierre et Marie Curie and my Diplôme d'Ingénieur from École Polytechnique.

Research Interests : 

• Stochastic Control Theory

• Stochastic Partial Differential Equations

• Partial Differential Equations

• Mathematical Finance

• Rough Paths

• Malliavin Calculus

• Online Learning

Grants : 

• NSF grant DMS-2406240 (2024-2027): $268,602

• NSF grant DMS-2007826 (2020-2024): $218,000

• FSU FYAP grant (2018): $20,000

Editorial Boards :

• Associate Editor: Finance and Stochastics

• Associate Editor: Applied Mathematics and Optimization

• Associate Editor: Advances in Continuous and Discrete Models 

Postdoc Mentorship : 

• Xihao He

• Guillermo Alvarez

• Eunjung Noh (2021-2023)

• Man Cheung Tsui (Teaching, 2021-2023)

• Patrick Heslin (Teaching, 2021-2023)

Ph.D. Supervision : 

• Lu Vy

• Liwei Huang

• Shreya Bose (graduated in 2023)

• Brad Mostowski (graduated in 2023)

Publications : 

• E. Bayraktar, I. Ekren, X. He, and X. Zhang, Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space, submitted.

• E. Bayraktar, I. Ekren, and H. Zhou, Uniform-in-time weak propogation of chaos for consensus-based optimization, submitted.

• E. Bayraktar, H. Cheung, I. Ekren, J. Qiu, H.M. Tai, and X. Zhang, Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space, submitted.

• R. Chhaibi, I. Ekren, and E. Noh, Solvability of the Gaussian Kyle model with imperfect information and risk aversion, submitted.

• I. Ekren and S. Nadtochiy, Identifiability implies consistency of MLE in partially observed diffusions on a torus, submitted. 

• G. Alvarez, I. Ekren, A. Kratsios, and X. Yang, Neural operators can play dynamics Stackelberg games, submitted.

• R. Chhaibi, I. Ekren, Eunjung Noh, and L. Vy, A unified approach to informed trading via Monge-Kantorovich duality, submitted.

• K. Back, F. Cocquemas, I. Ekren, and A. Lioui, Optimal transport and risk aversion in Kyle's model of informed trading, submitted. 

• E. Bayraktar, I. Ekren, and X. Zhang, Convergence rate of particle system for second-order PDEs in the Wasserstein space, accepted to SICON.

• I. Ekren, B. Mostowski, and G. Zitkovic, Kyle's model with stochastic liquidity, accepted to Finance and Stochastics.

• G. Alvarez, E. Bayraktar, I. Ekren, and L. Huang (2025), Sequential optimal contracting in continuous time, Frontiers of Mathematical Finance, Volume 4, pp. 114-139.

• E. Bayraktar, I. Ekren, and X. Zhang (2025), Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space, Communications in Partial Differential Equations, 2025, pp. 1-44.

• S. Bose and I. Ekren (2024), Multidimensional Kyle-Back model with a risk averse informed trader, SIAM Journal on Financial Mathematics, Volume 15.1, pp. 93-120.

• S. Bose and I. Ekren (2024), Kyle-Back Models with risk aversion and non-Gaussian beliefs, Annals of Applied Probability, Volume 33, No.6A, 4238-4271.

• E. Bayraktar, I. Ekren, and X. Zhang(2023) , A PDE approach for regret bounds under partial monitoring, Journal of Machine Learning Research 24(299), pp.1-24.

• E. Bayraktar, I. Ekren, and X. Zhang (2023), A smooth variational principle on the Wasserstein space, Proceeding of the AMS, Volume 151(09), 4089-4098.

• I. Ekren and S. Nadtochiy (2022), Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact, Mathematical Finance, 32(1), pp. 172-225. 

• E. Bayraktar, I. Ekren, and X. Zhang (2021), Prediction against limited adversary,  Journal of Machine Learning Research 22(72), pp.1-33.

• P. Bank, I. Ekren, and J. Muhle-Karbe (2021), Liquidity in competitive dealers market,  Mathematical Finance, 31(3), pp. 827-856.

• E. Bayraktar, T. Caye, and I. Ekren (2021), Asymptotics for Small Nonlinear Price Impact: a PDE Approach to the Multidimensional Case, Mathematical Finance, 31(1), pp. 36-108. 

• E. Bayraktar, I. Ekren, and Y. Zhang (2020), On the asymptotic optimality of comb strategy for prediction with expert advice, Annals of Applied Probability, Volume 30, No.6, 2517-2546.

  • Mathematica Appendix (Version December 2019). 

  • Mathematica Appendix (Version February 2019). 

• E. Bayraktar, I. Ekren, and X. Zhang (2020), Finite-time 4-Expert Prediction Problem, Communications in Partial Differential Equations, pp. 1-44. 

• R. Chhaibi and I. Ekren (2020), The Hormander condition for delayed stochastic differential equations, Annales Henri Lebesgue, Volume 3, pp. 1023 1048.

• I. Ekren and J. Muhle-Karbe (2019),  Portfolio choice with small temporary and transient price impact, Mathematical Finance, 29(4), pp. 1066-1115.

• I. Ekren and H. M. Soner, (2018), Constrained Optimal transport, Archive for Rational Mechanics and Analysis, Volume 227, Issue 3, pp. 929-965. 

• I. Ekren, R. Liu, and J. Muhle-Karbe, (2018), Optimal rebalancing frequency for multidimensional portfolios, Mathematics and Financial Economics, Volume 12, Issue 2, pp 165-191.

• I. Ekren, I. Kukavica, and M. Ziane, (2018),  Existence of invariant measures forthe stochastic damped KDV equation, Indiana University Mathematics Journal 67, 1221-1254.

• I. Ekren, I. Kukavica, and M. Ziane, (2017), Existence of invariant measures for some damped stochastic dispersive equations, Comptes Rendus Mathematique, Volume 355, Issue 6, 676-679.

• I. Ekren, (2017) Viscosity solutions of obstacle problems for Fully nonlinear path-dependent PDEs, Stochastic Processes and their Applications, Volume 127, Issue 12, 3966-3996.

• I. Ekren, I. Kukavica, and M. Ziane, (2017), Existence of invariant measures for the stochastic damped Schrodinger equation, Stoch PDE: Anal Comp. Volume 5, Issue 3, 343-367. 

• I. Ekren and J. Zhang, (2016), Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs, Probability, Uncertainty and Quantitative Risk 1:6  DOI 10.1186/s41546-016-0010-3.

• I. Ekren, N. Touzi, and J. Zhang, (2016), Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part II, Annals of Probability, Volume 44, Number 4, 2507-2553.

• I. Ekren, N. Touzi, and J. Zhang, (2016), Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part I, Annals of Probability, Volume 44, Number 2, 1212-1253.

• I. Ekren, N. Touzi, and J. Zhang, (2014), Optimal Stopping under Nonlinear Expectation, Stochastic Processes and their Applications, Volume 124, Issue 10, 3277-3311.

• I. Ekren, C. Keller, N. Touzi, and J. Zhang, (2014), On Viscosity Solutions of Path Dependent PDEs, Annals of Probability, Volume 42, Number 1, 204-236.