
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
EDITORIAL ACTIVITIES
Finance & Stochastics, Coeditor since January ’07, and
Associate Editor June ’00  December 06
Mathematical Finance, Associate Editor since Novembre ’03
Advances in Calculus of Variations, Associate Editor, January ’18 — December
‘22
Annals of Applied Probability,
Associate Editor since January ’13
Stochastic Processes and their
Applications, Associate Editor since January ’16
Stochastics:
an International Journal of Probability and Stochastic Processes,
Associate Editor since January ’16
Journal
of Optimization Theory and Applications, Associate Editor since
January ’14
Mathematical
Control and Related Fields, Associate Editor since September ’12
ParisPrinceton Lectures in
Mathematical Finance, Founder and CoEditor
Springer Briefs in Mathematical Finance, Associate Editor
Past editorial
activities:
Electronic Journal of Probability / Electronic
Communications in Probability, Associate
Editor June ’04  December
’14
SIAM Journal on Financial Mathematics, Associate
Editor January ’09  December
’12
Journal of Financial Econometrics, Associate
Editor January ’01  December
’06
Applied Mathematics Research
eXpress (AMRX), Associate Editor January ’04  December ’07
PhD Students
Present : Heythem Farhat,
Kaitong Hu, Hadrien De March.
Past: Gaoyue Guo (PostDoc, Oxford University), Zhenjie Ren (Assistant Professor, Université Paris Dauphine), Guillaume Royer (Bank of America, London), Emilie Fabre (Société Générale, Paris), Xiaolu Tan (Assistant Professor, Université Paris
Dauphine), Dylan Possamaï (Columbia
University), GillesEdouard Espinosa (BNPParibas),
Arash Fahim (Florida State University),
Arnaud Porchet (Goldman Sachs, London),
Romuald Elie (Professor, Université Marne
la Vallée), Fabian Astic (Moody’s NY),
Imen Ben Tahar (Assistant Professor,
Université Paris Dauphine), Amina Zeghal (Université Dauphine Tunis), Moez Mrad (Calyon, London), Bruno Bouchard (Professor, Université Paris Dauphine)
RECENT PAPERS
[106] Y. Lin, Z. Ren,
N. Touzi, J. Yang, Second order backward SDE with random terminal time, arXiv:1802.02260.
[105] P. HenryLabordère,
N. Touzi,
Branching diffusion representation for nonlinear Cauchy problems and Monte
Carlo approximation, (pdf file).
[104] H. De March, N. Touzi, Irreducible convex paving for
decomposition of multidimensional martingale transport plans, arXiv:1702.08298
[103] Z. Ren, N. Touzi, and J. Zhang, Comparison
of Viscosity Solutions of Semilinear PathDependent PDEs,
arXiv:1410.7281.
ACCEPTED PAPERS
[102] A.M.G. Cox, J. Obloj
and N. Touzi,
The Root solution to the multimarginal embedding problem: an optimal stopping
and timereversal approach, to appear in Probability Theory and Related Fields. arXiv:1505.03169
[101] P.
HenryLabordère, N. Oudjane,
X. Tan, N. Touzi, and X. Warin. Branching diffusion representation of semilinear
PDEs and Monte Carlo approximation, to appear in Annales de l'Institut Henri Poincaré (B)
Probabilités et Statistiques. (pdf file). arXiv:1603.01727 [math.PR]
[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. The Annals of Applied
Probability Vol. 27, No. 6, 1–37 (2017). (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. Annals of Probability 2017,
Vol. 45, No.
5, 3038–3074
DOI: 10.1214/16AOP1131. (pdf
file) 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, 2017, Vol. 27, No. 2, 686719. (pdf file)
[88] E. Fabre, G. Royer et N. Touzi. Liquidation of an indivisible asset with
independent investment. Mathematical
Finance, Volume 28, Issue 1 January 2018, pages 153–176 (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).