
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
[103] P. HenryLabordère, N. Oudjane, X.
Tan, N. Touzi, and X. Warin. Branching
diffusion representation of semilinear PDEs and Monte Carlo approximation, (pdf
file). arXiv:1603.01727 [math.PR]
[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] 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
[99] P. HenryLabordère, X. Tan and N. Touzi, Unbiased simulation of stochastic
differential equations. (pdf
file) arXiv:1504.06107 [math.PR]
[98] M. Beiglböck, P. HenryLabordère and N. Touzi, Monotone Martingale Transport Plans and
Skorohod Embedding (pdf file)
[97] A. Cosso, S. Federico, F. Gozzi, M.
Rosestolato, and N. Touzi,
Pathdependent equations and viscosity solutions in infinite dimension. (pdf
file)
[96] Z. Ren, N. Touzi, and J. Zhang, Comparison of Viscosity Solutions of
Semilinear PathDependent PDEs, arXiv:1410.7281.
ACCEPTED PAPERS
[95] G. Guo, X. Tan and N. Touzi, On the monotonicity principle of optimal Skorokhod embedding problem, 545 (2016), pp. 24782489. (pdf file)
[94] 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. (pdf file)
[93] G. Guo, X. Tan and N. Touzi, Optimal Skorokhod embedding under
finitelymany marginal constraints, SIAM
Journal on Control and Optimization 544 (2016), pp. 21742201.(pdf file)
[92] M. Beiglböck, M. Nutz and N. Touzi, Complete Duality for Martingale Optimal
Transport on the Line. To appear in Annals
of Probability. arXiv:1507.00671
[91] J. Cvitanic, D. Possamaï and N. Touzi, Moral hazard in dynamic risk management, Management Science, to appear. arXiv:1406.5852. (pdf
file)
[90] P. HenryLabordère, X. Tan and N. Touzi, An Explicit Version of the Onedimensional
Brenier’s Theorem with Full Marginals Constraint. Stochastic Processes and their Applications, to appear.
(pdf
file)
[89] S. Kallblad, X. Tan and N. Touzi, Optimal Skorokhod embedding given full
marginals and AzémaYor peacocks. Annals
of Applied Probability, to appear. (pdf
file)
[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, 2016, Vol.
44, No. 2, 12121253. 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).