Marcel Nutz

Marcel Nutz

Professor
Department of Statistics
Room 1031 SSW
1255 Amsterdam Avenue
New York, NY 10027
Phone (+1) 212-854-5165

Also affiliated with:

Department of Mathematics
Data Science Institute

mnutz@columbia.edu

Photo credit: Sara Kerens
Marcel’s research focuses on optimal transport, mathematical finance and game theory. He holds a PhD in mathematics from ETH Zurich.

Marcel was named IMS Fellow, Columbia-Ecole Polytechnique Alliance Professor, Alfred P. Sloan Fellow and co-Chair of the IMS-FIPS. He currently serves on the editorial boards of FMF, MF, MOR, SICON, SIFIN. He previously served on the board of SPA (2018-2024). Support by several NSF grants is gratefully acknowledged (CV).

Links

Google Scholar page
ArXiv page
CV
Seminars: Mathematical Finance, Applied Probability, Statistics, Probability

Courses

Introduction to Entropic Optimal Transport (in Paris)
Lecture notes: PDF

Publications and Preprints

M. Nutz:
Quadratically Regularized Optimal Transport: Existence and Multiplicity of Potentials
Preprint (submitted), 2024 [PDF, arXiv]

M. Nutz, J. Wiesel:
On the Martingale Schrödinger Bridge between Two Distributions
Preprint (submitted), 2024 [PDF, arXiv]

M. Nutz, K. Webster, L. Zhao:
Unwinding Stochastic Order Flow: When to Warehouse Trades
Preprint (submitted), 2023 [PDF, SSRN, arXiv]

Y. Yang, S. Eckstein, M. Nutz, S. Mandt:
Estimating the Rate-Distortion Function by Wasserstein Gradient Descent
37th Conference on Neural Information Processing Systems (NeurIPS), 2023 [PDF, arXiv, NeurIPS]

M. Nutz, A. Riveros Valdevenito:
On the Guyon-Lekeufack Volatility Model
Finance & Stochastics, forthcoming [PDF, arXiv]

P. Ghosal, M. Nutz:
On the Convergence Rate of Sinkhorn's Algorithm
Preprint (submitted), 2022 [PDF, arXiv]

M. Nutz, R. Wang, Z. Zhang:
Martingale Transports and Monge Maps
Annals of Applied Probability, forthcoming [PDF, arXiv]

S. Eckstein, M. Nutz:
Convergence Rates for Regularized Optimal Transport via Quantization
Mathematics of Operations Research, Vol. 49, No. 2, pp. 1223-1240, 2024. [PDF, arXiv, DOI]

M. Nutz, J. Wiesel, L. Zhao:
Martingale Schrödinger Bridges and Optimal Semistatic Portfolios
Finance & Stochastics, Vol. 27, No. 1, pp. 233-254, 2023 [PDF, arXiv, DOI]

M. Nutz, J. Wiesel, L. Zhao:
Limits of Semistatic Trading Strategies
Mathematical Finance, Vol. 33, No. 1, pp. 185-205, 2023 [PDF, arXiv, DOI]

M. Nutz, J. Wiesel:
Stability of Schrödinger Potentials and Convergence of Sinkhorn's Algorithm
Annals of Probability, Vol. 51, No. 2, pp. 699-722, 2023 [PDF, arXiv, DOI]

M. Nutz, Y. Zhang:
Mean Field Contest with Singularity
Mathematics of Operations Research, Vol. 48, No. 2, pp. 1095-1118, 2023 [PDF, arXiv, SSRN, DOI]

S. Eckstein, M. Nutz:
Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm
SIAM Journal on Mathematical Analysis, Vol. 54, No. 6, pp. 5922-5948, 2022 [PDF, arXiv, DOI]

P. Ghosal, M. Nutz, E. Bernton:
Stability of Entropic Optimal Transport and Schrödinger Bridges
Journal of Functional Analysis, Vol. 283, No. 9, Paper No. 109622, 2022. [PDF, arXiv, DOI]

M. Nutz, J. Wiesel:
Entropic Optimal Transport: Convergence of Potentials
Probability Theory and Related Fields, Vol. 184, pp. 401-424, 2022 [PDF, arXiv, DOI]

E. Bernton, P. Ghosal, M. Nutz:
Entropic Optimal Transport: Geometry and Large Deviations
Duke Mathematical Journal, Vol. 171, No. 16, pp. 3363-3400, 2022 [PDF, arXiv, DOI]

M. Nutz, F. Stebegg:
Climate Change Adaptation under Heterogeneous Beliefs
Mathematics and Financial Economics, Vol. 16, No. 3, pp. 481-508, 2022 [PDF, arXiv, SSRN, DOI]

M. Nutz, Y. Zhang:
Reward Design in Risk-Taking Contests
SIAM Journal on Financial Mathematics, Vol. 13, No. 1, pp. 129-146, 2022 [PDF, arXiv, SSRN, DOI]

M. Nutz, R. Wang:
The Directional Optimal Transport
Annals of Applied Probability, Vol. 32, No. 2, pp. 1400-1420, 2022 [PDF, arXiv, DOI]

M. Beiglböck, M. Nutz, F. Stebegg:
Fine Properties of the Optimal Skorokhod Embedding Problem
Journal of the European Mathematical Society (JEMS), Vol. 24, No. 4, pp. 1389-1429, 2022 [PDF, arXiv, DOI]

J. Muhle-Karbe, M. Nutz, X. Tan:
Asset Pricing with Heterogeneous Beliefs and Illiquidity
Mathematical Finance, Vol. 30, No. 4, pp. 1392-1421, 2020. [PDF, arXiv, SSRN, DOI]

M. Nutz, Y. Zhang:
Conditional Optimal Stopping: A Time-Inconsistent Optimization
Annals of Applied Probability, Vol. 30, No. 4, pp. 1669-1692, 2020. [PDF, arXiv, DOI]

M. Nutz, J.A. Scheinkman:
Shorting in Speculative Markets
Journal of Finance, Vol. 75, No. 2, pp. 995-1036, 2020. [PDF, SSRN, arXiv, DOI]

M. Nutz, J. San Martin, X. Tan:
Convergence to the Mean Field Game Limit: A Case Study
Annals of Applied Probability, Vol. 30, No. 1, pp. 259-286, 2020. [PDF, arXiv, DOI]

M. Nutz, F. Stebegg, X. Tan:
Multiperiod Martingale Transport
Stochastic Processes and their Applications, Vol. 130, No. 3, pp. 1568-1615, 2020. [PDF, arXiv, DOI]

M. Nutz, Y. Zhang:
A Mean Field Competition
Mathematics of Operations Research, Vol. 44, No. 4, pp. 1145-1509, 2019 [PDF, arXiv, DOI]

M. Nutz, F. Stebegg:
Canonical Supermartingale Couplings
Annals of Probability, Vol. 46, No. 6, pp. 3351-3398, 2018 [PDF, arXiv, DOI]

J. Muhle-Karbe, M. Nutz:
A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing
Finance & Stochastics, Vol. 22, No. 2, pp. 281-295, 2018 [PDF, arXiv, DOI]

M. Nutz:
A Mean Field Game of Optimal Stopping
SIAM Journal on Control and Optimization, Vol. 56, No. 2, pp. 1206-1221, 2018 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Robust Utility Maximization with Lévy Processes
Mathematical Finance, Vol. 28, No. 1, pp. 82-105, 2018 [PDF, arXiv, DOI]

J. Guyon, R. Menegaux, M. Nutz:
Bounds for VIX Futures given S&P 500 Smiles
Finance & Stochastics, Vol. 21, No. 3, pp. 593-630, 2017 [PDF, arXiv, DOI]

M. Beiglböck, M. Nutz, N. Touzi:
Complete Duality for Martingale Optimal Transport on the Line
Annals of Probability, Vol. 45, No. 5, pp. 3038-3074, 2017 [PDF, arXiv, DOI]

S. Biagini, B. Bouchard, C. Kardaras, M. Nutz:
Robust Fundamental Theorem for Continuous Processes
Mathematical Finance, Vol. 27, No. 4, pp. 963-987, 2017 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Nonlinear Lévy Processes and their Characteristics
Transactions of the American Mathematical Society, Vol. 369, No. 1, pp. 69-95, 2017 [PDF, arXiv, DOI]

B. Bouchard, M. Nutz:
Consistent Price Systems under Model Uncertainty
Finance & Stochastics, Vol. 20, No. 1, pp. 83-98, 2016 [PDF, arXiv, DOI]

B. Bouchard, M. Nutz:
Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions
Mathematics of Operations Research, Vol. 41, No. 1, pp. 109-124, 2016 [PDF, arXiv, DOI]

M. Nutz:
Utility Maximization under Model Uncertainty in Discrete Time
Mathematical Finance, Vol. 26, No. 2, pp. 252-268, 2016 [PDF, arXiv, DOI]

M. Nutz:
Robust Superhedging with Jumps and Diffusion
Stochastic Processes and their Applications,  Vol. 125, No. 12, pp. 4543-4555, 2015 [PDF, arXiv, DOI]

B. Bouchard, M. Nutz:
Arbitrage and Duality in Nondominated Discrete-Time Models
Annals of Applied Probability, Vol. 25, No. 2, pp. 823-859, 2015 [PDF, arXiv, DOI]

M. Nutz, J. Zhang:
Optimal Stopping under Adverse Nonlinear Expectation and Related Games
Annals of Applied Probability, Vol. 25, No. 5, pp. 2503-2534, 2015 [PDF, arXiv, DOI]

M. Beiglböck, M. Nutz:
Martingale Inequalities and Deterministic Counterparts
Electronic Journal of Probability, Vol. 19, No. 95, pp. 1-15, 2014 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Measurability of Semimartingale Characteristics with Respect to the Probability Law
Stochastic Processes and their Applications, Vol. 124, No. 11, pp. 3819-3845, 2014 [PDF, arXiv, DOI]

M. Nutz:
Superreplication under Model Uncertainty in Discrete Time
Finance & Stochastics, Vol. 18, No. 4, pp. 791-803, 2014 [PDF, arXiv, DOI]

B. Bouchard, L. Moreau, M. Nutz:
Stochastic Target Games with Controlled Loss
Annals of Applied Probability, Vol. 24, No. 3, pp. 899-934, 2014 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Superreplication under Volatility Uncertainty for Measurable Claims
Electronic Journal of Probability, Vol. 18, No. 48, pp. 1-14, 2013 [PDF, arXiv, DOI]

M. Nutz, R. van Handel:
Constructing Sublinear Expectations on Path Space
Stochastic Processes and their Applications, Vol. 123, No. 8, pp. 3100-3121, 2013 [PDF, arXiv, DOI]

M. Nutz:
Random G-Expectations
Annals of Applied Probability, Vol. 23, No. 5, pp. 1755-1777, 2013 [PDF, arXiv, DOI]

M. Nutz:
Pathwise Construction of Stochastic Integrals
Electronic Communications in Probability, Vol. 17, No. 24, pp. 1-7, 2012 [PDF, arXiv, DOI]

M. Nutz:
A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
Electronic Journal of Probability, Vol. 17, No. 23, pp. 1-23, 2012 [PDF, arXiv, DOI]

B. Bouchard, M. Nutz:
Weak Dynamic Programming for Generalized State Constraints
SIAM Journal on Control and Optimization, Vol. 50, No. 6, pp. 3344-3373, 2012 [PDF, arXiv, DOI]

Y. Dolinsky, M. Nutz, H.M. Soner:
Weak Approximation of G-Expectations
Stochastic Processes and their Applications, Vol. 122, No. 2, pp. 664-675, 2012 [PDF, arXiv, DOI]

M. Nutz, H.M. Soner:
Superhedging and Dynamic Risk Measures under Volatility Uncertainty
SIAM Journal on Control and Optimization, Vol. 50, No. 4, pp. 2065-2089, 2012 [PDF, arXiv, DOI]

M. Nutz:
Risk Aversion Asymptotics for Power Utility Maximization
Probability Theory and Related Fields, Vol. 152, No. 3-4, pp. 703-749, 2012 [PDF, arXiv, DOI]

M. Nutz:
Power Utility Maximization in Constrained Exponential Lévy Models
Mathematical Finance, Vol. 22, No. 4, pp. 690-709, 2012 [PDF, arXiv, DOI]

M. Nutz:
The Bellman Equation for Power Utility Maximization with Semimartingales
Annals of Applied Probability, Vol. 22, No. 1, pp. 363-406, 2012 [PDF, arXiv, DOI]

J. Muhle-Karbe, M. Nutz:
Small-Time Asymptotics of Option Prices and First Absolute Moments
Journal of Applied Probability, Vol. 48, No. 4, pp. 1003-1020, 2011 [PDF, arXiv, DOI]

M. Nutz:
The Opportunity Process for Optimal Consumption and Investment with Power Utility
Mathematics and Financial Economics, Vol. 3, No. 3, pp. 139-159, 2010 [PDF, arXiv, DOI]

M. Nutz:
Optimal Consumption and Investment with Power Utility
PhD Thesis ETH Zurich, Diss. ETH No. 19272, 2010 [PDF, DOI]
Last update: July 1, 2024