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 and SPA. 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 Schr÷dinger 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
Preprint (submitted), 2023 [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
Preprint (submitted), 2022 [PDF, arXiv]

S. Eckstein, M. Nutz:
Convergence Rates for Regularized Optimal Transport via Quantization
Mathematics of Operations Research, forthcoming [PDF, arXiv, DOI]

M. Nutz, J. Wiesel, L. Zhao:
Martingale Schr÷dinger 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 Schr÷dinger 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 Schr÷dinger 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. Beiglb÷ck, 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 LÚvy 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. Beiglb÷ck, 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 LÚvy 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. Beiglb÷ck, 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 LÚvy 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: April 11, 2024