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).

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
[84]
P. HenryLabordère
and N. Touzi, An
Explicit Martingale Version of Brenier's Theorem. (pdf file)
[83]
D. Possamaï,
N. Touzi and M. Soner, Homogenization
and asymptotics for small transaction costs: the
multidimensional case. arXiv:1212.6275
[82]
I. Ekren,
N. Touzi and J. Zhang, Viscosity Solutions of
Fully Nonlinear Parabolic Path Dependent PDEs: Part II,
arXiv:1210.0007v2[math.PR].
[81]
I. Ekren,
N. Touzi and J. Zhang, Viscosity Solutions of
Fully Nonlinear Parabolic Path Dependent PDEs: Part I,
arXiv:1210.0006v2[math.PR].
[80]
I. Ekren,
N. Touzi and J. Zhang, Optimal Stopping under
Nonlinear Expectation, arXiv:1209.6601v2[math.PR].
[79]
J. Obloj,
P. HenryLabordère, P. Spoida,
and N. Touzi, Maximum Maximum
of Martingales given Marginals. (pdf file)
[78]
R. Belaouar,
A. Fahim and N. Touzi, Optimal
Production Policy under Carbon Emission Market. (pdf file)
[77]
D. Possamaï,
G. Royer and N. Touzi, On
the robust superhedging of measurable claims. Electronic Communications in
Probability, to appear. arXiv:
1302.1850v2. (pdf file)
[76] P. HenryLabordère, X. Tan and N. Touzi,
A numerical algorithm for a class of BSDE via branching process.
Stochastic Processes and their Applications, to appear.
arXiv:1302.4624 [math.NA](pdf file)
[75] M. Soner and N. Touzi, Homogenization
and asymptotics for small transaction costs. SIAM Journal
on Control and Optimization, to appear (pdf file)
[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, to appear. (pdf file)
[73]
G.E. Espinosa
and N. Touzi,
Optimal Investment under Relative Performance Concerns. Mathematical Finance, to
appear. (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.
[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.
[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.
[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.
[44] M. Mrad, N. Touzi, and A. Zeghal, Monte
Carlo estimation of a joint density using Malliavin
calculus.
[43] M. Soner and N. Touzi, Hedging under gamma constraints by optimal
stopping and facelifting.
[42] R. Carmona and N. Touzi,
Optimal multiple stopping and valuation of swing options.
[41] B. Bouchard, N. El Karoui
and N. Touzi, Maturity randomisation for
stochastic control problems.
[40] P. Cheridito, M.
Soner and N. Touzi,
Small time path behavior of double stochastic
integrals and applications to stochastic control.
[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).
[35]
E. Jouini, M. Meddeb and N. Touzi,
Vectorvalued measure of risk, Finance and Stochastics,
8, 531552.
[34]
B. Bouchard, N. Touzi and A.
Zeghal, Dual Formulation of the Utility
Maximization Problem : the case of Nonsmooth
Utility.
[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.
[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).
[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.
[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).