
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] G. Guo, X. Tan and N. Touzi, On the
monotonicity principle of optimal Skorokhod embedding problem.
(pdf file)
[98] P. HenryLabordère, X. Tan and N.
Touzi, Unbiased
simulation of stochastic differential equations. (pdf
file) arXiv:1504.06107 [math.PR]
[97] M. Beiglböck, P. HenryLabordère and
N. Touzi,
Monotone Martingale Transport Plans and Skorohod Embedding (pdf file)
[96] A. Cosso, S. Federico, F. Gozzi, M.
Rosestolato, and N. Touzi, Pathdependent equations and viscosity solutions in infinite
dimension. (pdf
file)
[95] Z. Ren, N. Touzi, and J. Zhang, Comparison of
Viscosity Solutions of Semilinear PathDependent PDEs, arXiv:1410.7281.
ACCEPTED
PAPERS
[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. To appear in SIAM
Journal on Control and Optimization.(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).