
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
[93] S. Kallblad, X. Tan and N. Touzi, Optimal Skorokhod embedding given full
marginals and AzémaYor peacocks (pdf
file)
[92] M. Beiglböck, P. HenryLabordère and N. Touzi, Monotone Martingale Transport Plans and
Skorohod Embedding (pdf file)
[91] A. Cosso, F. Gozzi, M. Rosestolato, F.
Salvatore and N. Touzi, Pathdependent
equations and viscosity solutions in infinite dimension. (pdf
file)
[90] J. Ma, Z. Ren, N. Touzi and J. Zhang, Large Deviations for NonMarkovian
Diffusions and a PathDependent Eikonal Equation. (pdf
file)
[89] J. Cvitanic, D. Possamaï and N. Touzi, Moral hazard in dynamic risk management,
arXiv:1406.5852.
[88] P. HenryLabordère, X. Tan and N. Touzi, An Explicit Version of the Onedimensional
Brenier’s Theorem with Full Marginals Constraint. (pdf
file)
[87] P. HenryLabordère and N. Touzi, An Explicit Martingale Version of Brenier's Theorem. (pdf file)
[86] E. Fabre, G. Royer et N. Touzi. Liquidation of an indivisible asset with
independent investment. (pdf file).
[85] I. Ekren, N. Touzi and J. Zhang, Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part II, arXiv:1210.0007v2[math.PR].
ACCEPTED PAPERS
[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] J. Obloj, P. HenryLabordère, P. Spoida, and N. Touzi, Maximum Maximum of Martingales given Marginals, Annals of 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).