
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
[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, F. Gozzi, M. Rosestolato, F. Salvatore 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:1410.7291.
[90] J. Cvitanic,
D. Possamaï and N. Touzi, Moral hazard in dynamic risk management,
arXiv:1406.5852.
[89] P. HenryLabordère,
X. Tan and N. Touzi, An Explicit Version of the Onedimensional Brenier’s
Theorem with Full Marginals Constraint. (pdf
file)
[88] P. HenryLabordère
and N. Touzi, An
Explicit Martingale Version of Brenier's Theorem. (pdf
file)
[87] E. Fabre, G. Royer et N. Touzi. Liquidation of an indivisible
asset with independent investment. (pdf file).
ACCEPTED
PAPERS
[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, to appear. (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).