
Nizar Touzi Professor, Applied Mathematics

Centre de
Mathématiques Appliquées
Ecole
Polytechnique
UMR CNRS 7641
91128 Palaiseau Cedex
FRANCE
Téléphone: 
33 (0)169334612 
Fax: 
33 (0)169333011 
email: 
Actualités
* New Advances in Financial Mathematics, 4 avril 2013
* Bachelier Seminar, Institut Henri Poincaré, Paris
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, AprilJune 2010 (pdf file).
DISTINCTIONS
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, AprilJune 2010
Best Young Researcher in Finance Award 2007 of the Europlace Institute of Finance
RECENT PAPERS
[102] Z. Ren, N.
Touzi, and J. Zhang, Comparison of
viscosity solutions of fully nonlinear degenerate parabolic Pathdependent PDEs, (pdf file), arXiv: 1511.05910.
[101] J. Cvitanic,
D. Possamaï and N. Touzi, Dynamic programming approach to PrincipalAgent problems. (pdf
file)
[100] G. Guo, X.
Tan and N. Touzi, Tightness and duality
of martingale transport on the Skorokhod space. (pdf file)
[99] M. Beiglböck,
M. Nutz and N. Touzi, Complete Duality for Martingale Optimal Transport on the Line. arXiv:1507.00671
[98] A.M.G. Cox, J. Obloj
and N. Touzi, The Root solution to the
multimarginal embedding problem: an optimal stopping and timereversal
approach. arXiv:1505.03169
[97] G. Guo, X. Tan and N.
Touzi, On the monotonicity
principle of optimal Skorokhod embedding problem.
(pdf file)
[96] G. Guo, X. Tan and N.
Touzi, Optimal Skorokhod
embedding under finitelymany marginal constraints. (pdf file)
[95] P. HenryLabordère,
X. Tan and N. Touzi, Exact simulation of
multidimensional stochastic differential equations. (pdf
file)
[94] S. Kallblad, X. Tan
and N. Touzi, Optimal Skorokhod embedding given full marginals
and AzémaYor peacocks (pdf file)
[93] M. Beiglböck, P.
HenryLabordère and N. Touzi, Monotone Martingale Transport Plans and Skorohod
Embedding (pdf file)
[92] A. Cosso, S.
Federico, F. Gozzi, M. Rosestolato,
and N. Touzi, Pathdependent equations
and viscosity solutions in infinite dimension. (pdf
file)
[91] Z. Ren, N. Touzi, and
J. Zhang, Comparison of Viscosity
Solutions of Semilinear PathDependent PDEs, arXiv:1410.7281.
[90] J. Cvitanic, D. Possamaï and N. Touzi,
Moral hazard in dynamic risk management, arXiv:1406.5852.
(pdf file)
[89] P. HenryLabordère,
X. Tan and N. Touzi, An Explicit Version
of the Onedimensional Brenier’s Theorem with Full Marginals Constraint. (pdf
file)
ACCEPTED PAPERS
[88] E. Fabre, G. Royer et
N. Touzi. Liquidation
of an indivisible asset with independent investment. Mathematical Finance, to appear (pdf file).
[87] P. HenryLabordère
and N. Touzi, An Explicit Martingale
Version of Brenier's Theorem. Finance and Stochastics,
to appear. (pdf
file)
[86] J. Ma, Z. Ren, N.
Touzi and J. Zhang, Large Deviations for
NonMarkovian Diffusions and a PathDependent Eikonal Equation. Annales de l’IHP: Probabilités
et Statistique, to
appear. (pdf
file)
[85] I. Ekren, N. Touzi
and J. Zhang, Viscosity Solutions of Fully Nonlinear
Parabolic Path Dependent PDEs: Part II, Annals of Probability, to appear. arXiv:1210.0007v2[math.PR].
[84] 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
[83] J. Obloj, P. Spoida,
and N. Touzi, Martingale Inequalities
for the Maximum via Pathwise Arguments, Séminaires de Probabilités, to appear. (pdf
file)
[82] N. Touzi,
Martingale Inequalities, Optimal Martingale Transport, and Robust Superhedging, ESAIM:
Proceedings and Surveys, Vol. 45 (September 2014), Congrès SMAI 2013. (pdf file)
[81] Z. Ren, N. Touzi and
J. Zhang, An Overview of Viscosity
Solutions of Path Dependent PDEs, Stochastic Analysis and Applications, in Honnor
of Terry Lyons, Springer Proceedings in Mathematics and Statisctics.
(pdf file)
[80] P. HenryLabordère,
J. Obloj, P.
Spoida, and N. Touzi, Maximum Maximum of Martingales given Marginals, Annals
of Applied Probability, 2016, Vol. 26, No. 1, 1–44. (pdf file)
[79] I. Ekren, N. Touzi
and J. Zhang, Viscosity Solutions of Fully Nonlinear
Parabolic Path Dependent PDEs: Part I, Annals of Probability, to appear.
arXiv:1210.0006v2[math.PR].
[78] D. Possamaï, G. Royer
and N. Touzi, On the robust superhedging
of measurable claims. Electronic
Communications in Probability, 18(95):113, arXiv: 1302.1850v2. (pdf file)
[77] P. HenryLabordère,
X. Tan and N. Touzi, A numerical
algorithm for a class of BSDE via branching process. Stochastic Processes and their Applications 124:11121140, 2014. arXiv:1302.4624 [math.NA](pdf
file)
[76] M. Soner and N.
Touzi, Homogenization and asymptotics for small transaction costs. SIAM Journal on Control and Optimization,
51(4), 2893–2921. (2013) (pdf file)
[75] I. Ekren, N. Touzi
and J. Zhang, Optimal Stopping under
Nonlinear Expectation, Stochastic
Processes and Their Applications, 124 (2014),
32773311. arXiv:1209.6601v2[math.PR].
[74] A. Galichon, P.
HenryLabordère and N. Touzi, A stochastic control approach to noarbitrage bounds given marginals, with an application to Lookback
options. Annals of Applied
Probability, Volume 24, Number 1 (2014), 312336. (pdf file)
[73] G.E. Espinosa and N.
Touzi, Optimal Investment under Relative
Performance Concerns. Mathematical
Finance, Article first published online: 6 JUN 2013. (pdf
file)
[72] X. Tan and N. Touzi, Optimal Transportation under Controlled Stochastic Dynamics, Annals of Probability,
2013, Vol.
41, No. 5, 3201–324. (pdf file)
[71] I. Ekren, C. Keller,
N. Touzi and J. Zhang, On Viscosity
Solutions of Path Dependent PDEs, Annals of Probability, to appear. (pdf file)
[70] G.E. Espinosa and N.
Touzi, Detecting the Maximum of a
MeanReverting Scalar Diffusion, SIAM
Journal on Control and Optimization, to appear. (pdf
file)
[69] R. Carmona, F. Delarue, G.E.
Espinosa and N. Touzi, Singular
forwardbackward stochastic differential equations and emissions derivatives.
Annals of Applied Probability, to
appear. (pdf
file)
[68] M. Soner, N. Touzi
and J. Zhang, Dual Formulation of Second
Order Target Problems, Annals of
Applied Probability 23(1),
308347 (2013), arXiv:1003.6050. (pdf
file)
[67] D. Possamaï, M. Soner, and N. Touzi, Large
liquidity expansion of superhedging costs, Asymptotic Analysis, to appear. (pdf
file)
[66] M. Soner, N. Touzi
and J. Zhang, Quasisure Stochastic
Analysis through Aggregation, Electronic
Journal of Probability 16, 18441879 (2011), arXiv:1003.4431v1.
(pdf
file)
[65] Aïd R, G. Chemla, A. Porchet A. and N. Touzi (2011), Hedging and vertical integration in electricity markets. Management Science, Vol.
57, 8, 14381452, ISSN:00251909. (pdf file)
[64] B. Bouchard and N. Touzi, Weak Dynamic Programming Principle for Viscosity Solutions. SIAM Journal on Control and
Optimization, 49, 3, 948962 (2001). (pdf
file)
[63] M. Soner, N. Touzi
and J. Zhang, Wellposedness of second order backward SDEs, Probability
Theory and Related Fields, 153, 149–190. (pdf
file)
[62] M. Soner, N. Touzi
and J. Zhang, Martingale Representation
Theorem for the GExpectation, Stochastic Processes and their Applications
121, 265287. (pdf
file)
[61] R. Aïd, O. Féron, N. Touzi and C. Vialas, An arbitragefree interest rate model
consistent with economic constraints for longterm asset liability management, Bankers, Markets and Investors, to
appear. (pdf file)
[60] Fahim A, N. Touzi. and X. Warin, A
Probabilistic Numerical Scheme for Fully Nonlinear PDEs,
Annals of Applied Probability 21, 4, 13221364. (pdf file)
[59] I. Ben Tahar, M. Soner and N. Touzi, Merton
problem with taxes: characterization, computation and approximation, SIAM Journal on Financial Mathematics 1,
366395, (2010). (ps file)
[58] 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, 11331158. (pdf
file)
[57] B. Bouchard, R. Elie
and N. Touzi, Stochastic Target Problems
with Controlled Loss. SIAM Journal on
Control and Optimization, 48, 5,
pp. 31233150. (pdf file)
[56] R. Aïd, L. Campi, A. Nguyen Huu, and N.
Touzi, A Structural Risk Neutral Model
of Electricity Prices, International
Journal of Theoretical and Applied Finance 12, 7 (2009), 925947. (pdf
file)
[55] M. Soner and N.
Touzi, The dynamic programming equation
for second order stochastic target problems, SIAM Journal on Control and
Optimization 48, 4, 23442365. (pdf file)
[54] U. Cetin, M. Soner
and N. Touzi, Option hedging under
liquidity costs, Finance and Stochastics, 14, 317341. (pdf file)
[53] Elie R. and N. Touzi, Optimal lifetime consumption and investment under drawdown constraint. To Appear in Finance and Stochastics
12, 3 (July 2008), pp. 299330.
(pdf file)
[52] 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 4775 (2009). (pdf file)
[51] E. Jouini, W. Schachermayer and N. Touzi, Optimal risk sharing for law invariant monetary utility functions. Mathematical Finance 18, 2 (2008), pp.
269292. (pdf file)
[50] 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. 17791801. (pdf file)
[49] R. Elie, J.D. Fermanian and N. Touzi, Kernel estimation of Greek weights by
parameter randomization. Annals of Applied Probability 17, 4 (2007), 13991423. (pdf file)
[48] G. Carlier, I. Ekeland and N. Touzi, Optimal
derivatives design for meanvariance agents under adverse selection. Mathematics and Financial Economics, 1,
1 (April 2007), pp. 5780. (pdf file)
[47] F. Astic and N.
Touzi, No arbitrage conditions and
liquidity. Journal
of Mathematical Economics 43 (2007),
692708. (ps file)
[46] P. Cheridito, M. Soner, N. Touzi and Nicolas Victoir, Second Order Backward Stochastic
Differential Equations and Fully NonLinear Parabolic PDEs.
Communications in
Pure and Applied Mathematics 60 (7): 10811110 (2007). (pdf file)
[45] E. Jouini, W. Schachermayer and N. Touzi, Law Invariant Risk Measures have the Fatou
Property. Advances
in Mathematical Economics 9,
4972 (2006). (pdf file)
[44] M. Mrad, N. Touzi,
and A. Zeghal,
Monte Carlo estimation of a joint density using Malliavin
calculus. Computational
Economics 27, 4, 497531 (2006). (pdf file)
[43] M. Soner and N.
Touzi, Hedging under gamma constraints
by optimal stopping and facelifting. Mathematical Finance 17, 1, 5980 (2007). (pdf file)
[42] R. Carmona and N. Touzi, Optimal multiple stopping and valuation
of swing options. Mathematical Finance 18, 2 (April 2008) pp. 239268 (pdf file)
[41] B. Bouchard, N. El Karoui and N. Touzi, Maturity randomisation for stochastic control problems. Annals of Applied Probability, 15, 4, 25752605 (2005).
[40] 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, 24722495 (2005). (pdf file)
[39] P. Cheridito, M. Soner and N. Touzi,
The multidimensional superreplication problem under Gamma constraints, Annales de l’Institut
Henri Poincaré, Série C:
Analyse NonLinéaire 22,
633666
(2005). (pdf
file)
[38] A. Bensoussan, N.
Touzi and J.L. Menaldi, Penalty approximation and analytical
characterization of the problem of superreplication under portfolio
constraints, Asymptotic Analysis 41, 311330 (2005). (pdf file)
[37] B. Bouchard and N. Touzi, Discretetime approximation and Monte Carlo simulation of backward
stochastic differential equations, Stochastic
Processes and their Applications, 111, 175206 (2004). (pdf file)
[36] B. Bouchard, I. Ekeland
and N. Touzi, On the Malliavin
approach to Monte Carlo approximation of conditional expectations, Finance and Stochastics, 8, 4571 (2004). (pdf file)
[35] E. Jouini, M. Meddeb and N. Touzi,
Vectorvalued measure of risk, Finance
and Stochastics, 8, 531552. (pdf file)
[34] B. Bouchard, N. Touzi and A. Zeghal, Dual
Formulation of the Utility Maximization Problem : the
case of Nonsmooth Utility. Annals of Applied Probability, 14, 678717 (2004). (pdf file)
[33] H.M. Soner and N.
Touzi, The problem of superreplication
under constraints, to appear in ParisPrinceton
Lectures in Mathematical Finance, Lecture Notes in Mathematics, SpringerVerlag. (pdf file)
[32] H.M. Soner and N.
Touzi, Stochastic representation of mean
curvature type geometric flows, Annals
of Probability, 31, 11451165 (2003). (pdf file)
[31] H.M. Soner and N.
Touzi, Level set characterization of
stochastic target problems, Communications
in PDE’s, 27, 20312053. (pdf file)
[30] B. Bouchard, Y. Kabanov
and N. Touzi, Option pricing by large
risk aversion utility under transaction costs, Decision in Economics and Finance, 24, 127136 (2001).
[29] H.M. Soner and N.
Touzi, Dynamic programming for
stochastic target problems and geometric flows, Journal of the European Mathematical Society, 4, 201236 (2002). (pdf file)
[28] G. Deelstra, H. Pham and N. Touzi, Dual formulation of the utility maximization problem under transaction
costs, Annals of Applied Probability,
11 (4), 13531383 (2002).
[27] N. Touzi and N. Vieille, Continuoustime Dynkin games with mixed
strategies, SIAM Journal on Control
and Optimization 41, 10731088 (2002). (pdf file)
[26] H.M. Soner and N. Touzi,
Stochastic target problems, dynamic programming and viscosity solutions, SIAM Journal on Control and Optimization, 41, 404424 (2002). (pdf file)
[25] N. Touzi, Superreplication under proportional
transaction costs: from discrete to continuoustime models, Mathematical Methods of Operations Research
50, 297320 (1999).
[24] B. Bouchard and N. Touzi,
Explicit solution of the multivariate superreplication problem under transaction
costs, Annals of Applied Probability
10, 685708 (2000).
[23] N. Touzi, Direct
characterization of the value of superreplication under stochastic volatility
and portfolio constraints, Stochastic Processes and their Applications 88, 305328 (2000).
[22] H.M. Soner and N. Touzi, Superreplication under Gamma constraint, Journal on Control and Optimization 39, 7396 (2000).
[21] P.F. Koehl, H.
Pham and N. Touzi, On superreplication
under Transaction costs in general discretetime models, Theory of Probability and its Applications
45, 783788 (1999).
[20] L. Carassus, H. Pham and N. Touzi, Arbitrage and domination cost in a
discretetime model with convex portfolio constraints, Mathematical Finance, to appear.
[19] E. Jouini, P.F. Koehl and N. Touzi,
Optimal investment with taxes: an existence result, Journal of Mathematical Economics, 33, 373388.
[18] 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, 3156 (1999).
[17] N. Touzi, Optimal insurance
demand under marked point processes shocks, Annals of Applied Probability 10, 283312 (2000).
[16] J. Cvitanic, H. Pham and N. Touzi, Superreplication in stochastic volatility
models with portfolio constraints, Journal
of Applied Probability 36, 523545 (1999).
[15] J. Cvitanic, H. Pham and N. Touzi, A closedform solution for the problem of
superreplication under transaction costs, Finance and Stochastics 3, 3554 (1999).
[14] 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).
[13] 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, 391412 (1999).
[12] P.F. Koehl, H.
Pham and N. Touzi, Hedging in
discretetime under Transaction costs and continuoustime limit, Journal of Applied Probability 36,
163178 (1999).
[11] H. Pham and N. Touzi, The
fundamental theorem of asset pricing with cone constraints, Journal of Mathematical Economics, to
appear.
[10] N. Touzi, American options
exercise boundary when the volatility changes randomly, Applied Mathematics and Optimization 39,
411422 (1999).
[9] E. Fournié,
J. Lebuchoux and N. Touzi, Small Noise
Expansion and Importance Sampling, Asymptotic Analysis 14, 361376 (1997).
[8] E. Jouini, P.F. Koehl and N. Touzi,
Incomplete Markets, Transaction costs and Liquidity effects, European Journal of Finance 4, 325348.
[7] L.P. Hansen, J.A. Scheinkman and N. Touzi, Spectral Methods for Identifying Scalar
Diffusions, Journal of Econometrics
86, 132.
[6] J.P. Florens, E.
Renault and N. Touzi, Testing Embeddability by Stationary Reversible ContinuousTime
Markov Processes, Econometric Theory
14.
[5] 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.
[4] S. Pastorello,
E. Renault and N. Touzi, Statistical Inference for Random Variance
Option Pricing, Journal of Business and Economic Statistics, to appear.
[3] M. Romano and N. Touzi,
Contingent Claims and Market Completeness in a Stochastic Volatility Model, Mathematical Finance 7, 399412 (1997).
[2] H. Pham and N. Touzi,
Equilibrium State Prices in a Stochastic Volatility Model, Mathematical Finance 6, 215236 (1996).
[1] E. Renault and N. Touzi, Option Hedging and Implicit Volatilities, Mathematical Finance 6, 279302 (1996).