Ibrahim Ekren

I am an Associate Professor in the Department of Mathematics at the University of Michigan. Here is my latest CV and you may find my google scholar page here.

Contact Information :

Email: iekren@umich.edu

Address: University of Michigan, Department of Mathematics, 530 Church St, Ann Arbor, MI 48109

Office: 2856 East Hall

Previous Positions

2018-2023, Assistant Professor, Department of Mathematics, Florida State University.

2017-2018, Byrne Postdoctoral Assistant Professor, Department of Mathematics, University of Michigan. 

2014-2017, Postdoctoral researcher, Department of Mathematics, ETH Zurich. 

Education

I obtained my PhD in mathematics from the Department of Mathematics at the University of Southern California, where I worked under the supervision of Jianfeng Zhang. I received my master's degree from Université Pierre et-Marie-Curie, Paris, France and Diplome d'ingenieur from Ecole 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-2007826 (2020-2023): $218,000

• FSU FYAP grant (2018): $20,000

Postdoc Mentorship : 

• Eunjung Noh 

• Man Cheung Tsui (Teaching)

• Patrick Heslin (Teaching)

Ph.D. Supervision : 

• Lu Vy

• Liwei Huang

• Shreya Bose (graduated in 2023)

• Brad Mostowski (graduated in 2023)

Publications : 

• E. Bayraktar, I. Ekren, and X. Zhang, Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space, submitted.

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

• E. Bayraktar, I. Ekren, and X. Zhang, A smooth variational principle on the Wasserstein space, submitted.

• E. Bayraktar, I. Ekren, and X. Zhang, A PDE approach for regret bounds under partial monitoring, submitted.

• I. Ekren, B. Mostowski, and G. Zitkovic, Kyle's model with stochastic liquidity, submitted.

• S. Bose and I. Ekren, Multidimensional Kyle-Back model with a risk averse informed trader, submitted.

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

• S. Bose and I. Ekren, Kyle-Back Models with risk aversion and non-Gaussian beliefs, to appear in Annals of Applied Probability.

• 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 delayedstochastic 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 forMultidimensional 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.