Professor, Applied Mathematics
Centre de Mathématiques Appliquées
UMR CNRS 7641
91128 Palaiseau Cedex
Chaînes de Markov et martingales en temps discret, Ecole Polytechnique, 2ème année, PA Mathématiques Appliquées (pdf file)
Stochastic Calculus in Finance, Ecole Polytechnique, 3ème année, PA Mathématiques Appliquées (pdf file)
Deterministic and Stochastic Control, Application to Finance, Master Probabilité et Finance Ecole Polytechnique – Université Paris 6 (pdf file)
Optimal Stochastic Control, Stochastic Target Problems, and Backward SDEs, Lecture Notes of my lectures at the Fields Institute, April-June 2010 (pdf file).
ICM 2010 (Hyderabad) Invited Session Speaker (pdf file)
ERC Advanced Grant 2012
French Academy of Science – Natixis Foudation, Louis Bachelier Prize 2012
The University of Toronto Dean’s Distinguished Visitor Chair, Fields Institute, April-June 2010
Best Young Researcher in Finance Award 2007 of the Europlace Institute of Finance
Finance & Stochastics, Co-editor since January ’07, and Associate Editor June ’00 - December 06
Mathematical Finance, Associate Editor since Novembre ’03
Advances in Calculus of Variations, Associate Editor, January ’18 — December ‘22
Annals of Applied Probability, Associate Editor since January ’13
Stochastic Processes and their Applications, Associate Editor since January ’16
Stochastics: an International Journal of Probability and Stochastic Processes, Associate Editor since January ’16
Journal of Optimization Theory and Applications, Associate Editor since January ’14
Mathematical Control and Related Fields, Associate Editor since September ’12
Paris-Princeton Lectures in Mathematical Finance, Founder and Co-Editor
Springer Briefs in Mathematical Finance, Associate Editor
Past editorial activities:
Electronic Journal of Probability / Electronic Communications in Probability, Associate Editor June ’04 - December ’14
SIAM Journal on Financial Mathematics, Associate Editor January ’09 - December ’12
Journal of Financial Econometrics, Associate Editor January ’01 - December ’06
Applied Mathematics Research eXpress (AMRX), Associate Editor January ’04 - December ’07
Present : Heythem Farhat, Kaitong Hu, Hadrien De March.
Past: Gaoyue Guo (Post-Doc, Oxford University), Zhenjie Ren (Assistant Professor, Université Paris Dauphine), Guillaume Royer (Bank of America, London), Emilie Fabre (Société Générale, Paris), Xiaolu Tan (Assistant Professor, Université Paris Dauphine), Dylan Possamaï (Columbia University), Gilles-Edouard Espinosa (BNPParibas), Arash Fahim (Florida State University), Arnaud Porchet (Goldman Sachs, London), Romuald Elie (Professor, Université Marne la Vallée), Fabian Astic (Moody’s NY), Imen Ben Tahar (Assistant Professor, Université Paris Dauphine), Amina Zeghal (Université Dauphine Tunis), Moez Mrad (Calyon, London), Bruno Bouchard (Professor, Université Paris Dauphine)
 Y. Lin, Z. Ren, N. Touzi, J. Yang, Second order backward SDE with random terminal time, arXiv:1802.02260.
 P. Henry-Labordère, N. Touzi, Branching diffusion representation for nonlinear Cauchy problems and Monte Carlo approximation, (pdf file).
 H. De March, N. Touzi, Irreducible convex paving for decomposition of multi-dimensional martingale transport plans, arXiv:1702.08298
 Z. Ren, N. Touzi, and J. Zhang, Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs, arXiv:1410.7281.
 A.M.G. Cox, J. Obloj and N. Touzi, The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach, to appear in Probability Theory and Related Fields. arXiv:1505.03169
 P. Henry-Labordère, N. Oudjane, X. Tan, N. Touzi, and X. Warin. Branching diffusion representation of semilinear PDEs and Monte Carlo approximation, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. (pdf file). arXiv:1603.01727 [math.PR]
 J. Cvitanic, D. Possamaï and N. Touzi, Dynamic programming approach to Principal-Agent problems. Finance and Stochastics, to appear. arXiv:1510.07111
 Z. Ren, N. Touzi, and J. Zhang, Comparison of viscosity solutions of fully nonlinear degenerate parabolic Path-dependent PDEs, SIAM Journal on Mathematical Analysis, to appear. (pdf file), arXiv: 1511.05910.
 A. Cosso, S. Federico, F. Gozzi, M. Rosestolato, and N. Touzi, Path-dependent equations and viscosity solutions in infinite dimension. Annals of Probability, to appear. (pdf file)
 P. Henry-Labordère, X. Tan and N. Touzi, Unbiased simulation of stochastic differential equations. The Annals of Applied Probability Vol. 27, No. 6, 1–37 (2017). (pdf file) arXiv:1504.06107 [math.PR]
 M. Beiglböck, P. Henry-Labordère and N. Touzi, Monotone Martingale Transport Plans and Skorohod Embedding. To appear in Stochastic Processes and their Applications. (pdf file)
 G. Guo, X. Tan and N. Touzi, On the monotonicity principle of optimal Skorokhod embedding problem, SIAM Journal on Control and Optimization 54-5 (2016), pp. 2478-2489. (pdf file)
 G. Guo, X. Tan and N. Touzi, Tightness and duality of martingale transport on the Skorokhod space. To appear in Stochastic Processes and their Applications.
M. Beiglböck, M. Nutz and N. Touzi,
Complete Duality for Martingale Optimal Transport on the Line. Annals of Probability 2017,
Vol. 45, No.
DOI: 10.1214/16-AOP1131. (pdf file) arXiv:1507.00671
 P. Henry-Labordère, X. Tan and N. Touzi, An Explicit Version of the One-dimensional Brenier’s Theorem with Full Marginals Constraint. Stochastic Processes and their Applications, 126(9):2800-2834, 2016. (pdf file)
 D. Possamaï, M. Soner and N. Touzi, Homogenization and asymptotics for small transaction costs: the multidimensional case. Communications in Partial Differential Equations, to appear. arXiv:1212.6275
 J. Obloj, P. Spoida, and N. Touzi, Martingale Inequalities for the Maximum via Pathwise Arguments, Séminaires de Probabilités XLVII, Lecture Notes in Mathematics 2137, Springer, pp 227--248., to appear. (pdf file)
 Z. Ren, N. Touzi and J. Zhang, An Overview of Viscosity Solutions of Path Dependent PDEs, In Stochastic Analysis and Applications 2014, in Honour of Terry Lyons, Springer Proceedings in Mathematics and Statisctics, Volume 100, pp 397--454. (pdf file)
 P. Henry-Labordère, X. Tan and N. Touzi, A numerical algorithm for a class of BSDE via branching process. Stochastic Processes and their Applications 124:1112-1140, 2014. arXiv:1302.4624 [math.NA]
 R. Aïd, O. Féron, N. Touzi and C. Vialas, An arbitrage-free interest rate model consistent with economic constraints for long-term asset liability management, Bankers, Markets and Investors, to appear. (pdf file)
 D. Crisan, K. Manolarakis and N. Touzi, On the Monte Carlo simulation of Backward SDES: an improvement on the Malliavin weights, Stochastic Processes and Their Applications 120 (2010), no. 7, 1133-1158. (pdf file)
 Porchet A., N. Touzi and X. Warin, Valuation of a powerplant under production constraints and markets incompleteness. Mathematical Methods of Operations research, Volume 70, Issue 1 (2009), Page 47-75 (2009). (pdf file)
 I. Ben Tahar, M. Soner and N. Touzi, The dynamic programming equation for the problem of optimal investment under capital gains taxes. SIAM Journal on Control and Optimization 46, 5 (2007), pp. 1779-1801. (pdf file)
 P. Cheridito, M. Soner, N. Touzi and Nicolas Victoir, Second Order Backward Stochastic Differential Equations and Fully Non-Linear Parabolic PDEs. Communications in Pure and Applied Mathematics 60 (7): 1081-1110 (2007). (pdf file)
 P. Cheridito, M. Soner and N. Touzi, Small time path behavior of double stochastic integrals and applications to stochastic control. Annals of Applied Probability 15, 4, 2472-2495 (2005). (pdf file)
 P. Cheridito, M. Soner and N. Touzi, The multi-dimensional super-replication problem under Gamma constraints, Annales de l’Institut Henri Poincaré, Série C: Analyse Non-Linéaire 22, 633-666 (2005). (pdf file)
 A. Bensoussan, N. Touzi and J.-L. Menaldi, Penalty approximation and analytical characterization of the problem of super-replication under portfolio constraints, Asymptotic Analysis 41, 311-330 (2005). (pdf file)
 B. Bouchard and N. Touzi, Discrete-time approximation and Monte Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, 111, 175-206 (2004). (pdf file)
 H.M. Soner and N. Touzi, The problem of super-replication under constraints, to appear in Paris-Princeton Lectures in Mathematical Finance, Lecture Notes in Mathematics, Springer-Verlag. (pdf file)
H.M. Soner and N. Touzi, Dynamic programming for stochastic target
problems and geometric flows, Journal of the European Mathematical Society, 4, 201-236 (2002). (pdf file)
 G. Deelstra, H. Pham and N. Touzi, Dual formulation of the utility maximization problem under transaction costs, Annals of Applied Probability, 11 (4), 1353-1383 (2002).
 N. Touzi and N. Vieille, Continuous-time Dynkin games with mixed strategies, SIAM Journal on Control and Optimization 41, 1073-1088 (2002). (pdf file)
 H.M. Soner and N. Touzi, Stochastic target problems, dynamic programming and viscosity solutions, SIAM Journal on Control and Optimization, 41, 404-424 (2002). (pdf file)
 N. Touzi, Super-replication under proportional transaction costs: from discrete to continuous-time models, Mathematical Methods of Operations Research 50, 297-320 (1999).
 B. Bouchard and N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, Annals of Applied Probability 10, 685-708 (2000).
 N. Touzi, Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints, Stochastic Processes and their Applications 88, 305-328 (2000).
 H.M. Soner and N. Touzi, Super-replication under Gamma constraint, Journal on Control and Optimization 39, 73-96 (2000).
 P.-F. Koehl, H. Pham and N. Touzi, On super-replication under Transaction costs in general discrete-time models, Theory of Probability and its Applications 45, 783-788 (1999).
 L. Carassus, H. Pham and N. Touzi, Arbitrage and domination cost in a discrete-time model with convex portfolio constraints, Mathematical Finance, to appear.
 E. Jouini, P.-F. Koehl and N. Touzi, Optimal investment with taxes: an existence result, Journal of Mathematical Economics, 33, 373-388.
E. Jouini, P.-F. Koehl and N. Touzi, Optimal investment with taxes~: an optimal
control problem with endogeneous delay, Nonlinear
Analysis~: Theory, Methods and Applications 37, 31-56 (1999).
 N. Touzi, Optimal insurance demand under marked point processes shocks, Annals of Applied Probability 10, 283-312 (2000).
 J. Cvitanic, H. Pham and N. Touzi, Super-replication in stochastic volatility models with portfolio constraints, Journal of Applied Probability 36, 523-545 (1999).
 J. Cvitanic, H. Pham and N. Touzi, A closed-form solution for the problem of super-replication under transaction costs, Finance and Stochastics 3, 35-54 (1999).
 E. Fournié, J.M. Lasry and N. Touzi, Monte Carlo Methods in Stochastic Volatility Models, in Numerical Methods in Financial Mathematics, edited by C. Rogers et D. Talay, Cambridge University Press (1997).
 E. Fournié, J.M. Lasry, J. Lebuchoux, P.-L. Lions and N. Touzi, Some applications of Malliavin calculus to Monte Carlo methods in finance, Finance and Stochastics 3, 391-412 (1999).
 P.-F. Koehl, H. Pham and N. Touzi, Hedging in discrete-time under Transaction costs and continuous-time limit, Journal of Applied Probability 36, 163-178 (1999).
 H. Pham and N. Touzi, The fundamental theorem of asset pricing with cone constraints, Journal of Mathematical Economics, to appear.
 N. Touzi, American options exercise boundary when the volatility changes randomly, Applied Mathematics and Optimization 39, 411-422 (1999).
 E. Fournié, J. Lebuchoux and N. Touzi, Small Noise Expansion and Importance Sampling, Asymptotic Analysis 14, 361-376 (1997).
 E. Jouini, P.-F. Koehl and N. Touzi, Incomplete Markets, Transaction costs and Liquidity effects, European Journal of Finance 4, 325-348.
 L.P. Hansen, J.A. Scheinkman and N. Touzi, Spectral Methods for Identifying Scalar Diffusions, Journal of Econometrics 86, 1-32.
 J.-P. Florens, E. Renault and N. Touzi, Testing Embeddability by Stationary Reversible Continuous-Time Markov Processes, Econometric Theory 14.
 C. Gouriéroux, E. Renault and N. Touzi, Calibration by Simulation for Small Sample Bias Correction, in Simulation Based Inference in Econometrics Methods, edited by J. Geweke and R. Mariano.
 S. Pastorello, E. Renault and N. Touzi, Statistical Inference for Random Variance Option Pricing, Journal of Business and Economic Statistics, to appear.
 M. Romano and N. Touzi, Contingent Claims and Market Completeness in a Stochastic Volatility Model, Mathematical Finance 7, 399-412 (1997).
 H. Pham and N. Touzi, Equilibrium State Prices in a Stochastic Volatility Model, Mathematical Finance 6, 215-236 (1996).