
Nizar Touzi
Professor, Applied Mathematics

Centre de Mathématiques Appliquées
Ecole Polytechnique
UMR CNRS 7641
91128 Palaiseau Cedex
FRANCE
Actualités
* New
Advances in Financial Mathematics, 4 avril 2013
*
Bachelier Seminar, Institut Henri Poincaré, Paris
Lecture Notes
Distinctions
Recent
Papers
Accepted Papers
LECTURE NOTES
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] 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
[101] Z. Ren, N. Touzi, and J. Zhang, Comparison of
Viscosity Solutions of Semilinear PathDependent PDEs, arXiv:1410.7281.
ACCEPTED
PAPERS
[100] J.
Cvitanic, D. Possamaï and N. Touzi, Dynamic programming approach to PrincipalAgent
problems. Finance
and Stochastics, to appear. arXiv:1510.07111
[99] Z. Ren,
N. Touzi, and J. Zhang, Comparison of viscosity solutions of fully nonlinear degenerate
parabolic Pathdependent PDEs, SIAM Journal on Mathematical Analysis, to
appear. (pdf file), arXiv: 1511.05910.
[98] A. Cosso, S. Federico, F. Gozzi, M.
Rosestolato, and N. Touzi, Pathdependent equations and viscosity solutions in infinite
dimension. Annals
of Probability, to appear. (pdf
file)
[97] P. HenryLabordère, X. Tan and N.
Touzi, Unbiased
simulation of stochastic differential equations. To appear in Annals of Applied
Probability. (pdf
file) arXiv:1504.06107 [math.PR]
[96] M. Beiglböck, P. HenryLabordère and
N. Touzi,
Monotone Martingale Transport Plans and Skorohod Embedding. To appear in Stochastic
Processes and their Applications. (pdf
file)
[95] G. Guo,
X. Tan and N. Touzi, On the monotonicity principle of optimal Skorokhod embedding problem, SIAM Journal on Control and
Optimization 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, 126(9):28002834, 2016. (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, July
2016, Volume 20, Issue 3, pp
635–668. (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 XLVII, Lecture Notes in Mathematics 2137, Springer,
pp 227248., 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, In Stochastic Analysis and Applications 2014, in Honour
of Terry Lyons, Springer Proceedings in Mathematics and Statisctics, Volume
100, pp 397454. (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).
(pdf file)
[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).