izar Touzi               

  

 

Nizar Touzi

Professor, Applied Mathematics


 

 

 

Centre de Mathématiques Appliquées

Ecole Polytechnique

UMR CNRS 7641

91128 Palaiseau Cedex

FRANCE

 

 

 

Téléphone:

33 (0)1-69-33-46-12

Fax:

33 (0)1-69-33-30-11

e-mail:

nizar.touzi@polytechniqueDOTedu

 

 

 


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, April-June 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, April-June 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 Azéma-Yor peacocks (pdf file)

[92] M. Beiglböck, P. Henry-Labordère and N. Touzi, Monotone Martingale Transport Plans and Skorohod Embedding (pdf file)

[91] A. Cosso, F. Gozzi, M. Rosestolato, F. Salvatore and N. Touzi, Path-dependent equations and viscosity solutions in infinite dimension. (pdf file)

[90] J. Ma, Z. Ren, N. Touzi and J. Zhang, Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation. (pdf file)

[89] J. Cvitanic, D. Possamaï and N. Touzi, Moral hazard in dynamic risk management, arXiv:1406.5852.

[88] P. Henry-Labordère, X. Tan and N. Touzi, An Explicit Version of the One-dimensional Brenier’s Theorem with Full Marginals Constraint. (pdf file)

[87] P. Henry-Labordère 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).

 


ACCEPTED PAPERS

 

[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] J. Obloj, P. Henry-Labordère, 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):1-13, arXiv: 1302.1850v2. (pdf file)

[77] P. Henry-Labordère, X. Tan and N. Touzi, A numerical algorithm for a class of BSDE via branching process. Stochastic Processes and their Applications 124:1112-1140, 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), 3277-3311. arXiv:1209.6601v2[math.PR].

[74] A. Galichon, P. Henry-Labordère and N. Touzi, A stochastic control approach to no-arbitrage bounds given marginals, with an application to Lookback options. Annals of Applied Probability, Volume 24, Number 1 (2014), 312-336. (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 Mean-Reverting Scalar Diffusion, SIAM Journal on Control and Optimization, to appear. (pdf file)

[69] R. Carmona, F. Delarue, G.-E. Espinosa and N. Touzi, Singular forward-backward 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), 308-347 (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, Quasi-sure Stochastic Analysis through Aggregation, Electronic Journal of Probability 16, 1844-1879 (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, 1438-1452, ISSN:0025-1909. (pdf file)

[64] B. Bouchard and N. Touzi, Weak Dynamic Programming Principle for Viscosity Solutions. SIAM Journal on Control and Optimization, 49, 3, 948-962 (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 G-Expectation, Stochastic Processes and their Applications 121, 265-287. (pdf file)

[61] R. Aïd, O. Féron, N. Touzi and C. Vialas, An arbitrage-free interest rate model consistent with economic constraints for long-term 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, 1322-1364. (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, 366-395, (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, 1133-1158. (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. 3123-3150. (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), 925-947. (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, 2344-2365. (pdf file)

[54] U. Cetin, M. Soner and N. Touzi, Option hedging under liquidity costs, Finance and Stochastics, 14, 317-341. (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. 299-330. (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 47-75 (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. 269-292. (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. 1779-1801. (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), 1399-1423. (pdf file)

[48] G. Carlier, I. Ekeland and N. Touzi, Optimal derivatives design for mean-variance agents under adverse selection. Mathematics and Financial Economics, 1, 1 (April 2007), pp. 57-80. (pdf file)

[47] F. Astic and N. Touzi, No arbitrage conditions and liquidity. Journal of Mathematical Economics 43 (2007), 692-708. (ps file)

[46] P. Cheridito, M. Soner, N. Touzi and Nicolas Victoir, Second Order Backward Stochastic Differential Equations and Fully Non-Linear Parabolic PDEs. Communications in Pure and Applied Mathematics 60 (7): 1081-1110 (2007). (pdf file)

[45] E. Jouini, W. Schachermayer and N. Touzi, Law Invariant Risk Measures have the Fatou Property. Advances in Mathematical Economics 9, 49-72 (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, 497-531 (2006).  (pdf file)

[43] M. Soner and N. Touzi, Hedging under gamma constraints by optimal stopping and face-lifting. Mathematical Finance 17, 1, 59-80 (2007). (pdf file)

[42] R. Carmona and N. Touzi, Optimal multiple stopping and valuation of swing options. Mathematical Finance 18, 2 (April 2008) pp. 239-268 (pdf file)

[41] B. Bouchard, N. El Karoui and N. Touzi, Maturity randomisation for stochastic control problems. Annals of Applied Probability, 15, 4, 2575-2605 (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, 2472-2495 (2005). (pdf file)

[39] P. Cheridito, M. Soner and N. Touzi, The multi-dimensional super-replication problem under Gamma constraints, Annales de l’Institut Henri Poincaré, Série C: Analyse Non-Linéaire 22, 633-666 (2005). (pdf file)

[38] A. Bensoussan, N. Touzi and J.-L. Menaldi, Penalty approximation and analytical characterization of the problem of super-replication under portfolio constraints, Asymptotic Analysis 41, 311-330 (2005). (pdf file)

[37] B. Bouchard and N. Touzi, Discrete-time approximation and Monte Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, 111, 175-206 (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, 45-71 (2004).  (pdf file)

[35] E. Jouini, M. Meddeb and N. Touzi, Vector-valued measure of risk, Finance and Stochastics, 8, 531-552. (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, 678-717 (2004). (pdf file)

[33] H.M. Soner and N. Touzi, The problem of super-replication under constraints, to appear in Paris-Princeton Lectures in Mathematical Finance, Lecture Notes in Mathematics, Springer-Verlag. (pdf file)

[32] H.M. Soner and N. Touzi, Stochastic representation of mean curvature type geometric flows, Annals of Probability, 31, 1145-1165 (2003). (pdf file)

[31] H.M. Soner and N. Touzi, Level set characterization of stochastic target problems, Communications in PDE’s, 27, 2031-2053. (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, 127-136 (2001).

[29] H.M. Soner and N. Touzi, Dynamic programming for stochastic target problems and geometric flows, Journal of the European Mathematical Society, 4, 201-236 (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), 1353-1383 (2002).
[27]
N. Touzi and N. Vieille, Continuous-time Dynkin games with mixed strategies, SIAM Journal on Control and Optimization 41, 1073-1088 (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, 404-424 (2002). (pdf file)
[25]
N. Touzi, Super-replication under proportional transaction costs: from discrete to continuous-time models, Mathematical Methods of Operations Research 50, 297-320 (1999).
[24]
B. Bouchard and N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, Annals of Applied Probability 10, 685-708 (2000).
[23]
N. Touzi, Direct characterization of the value of super-replication under stochastic volatility and portfolio constraints, Stochastic Processes and their Applications 88, 305-328 (2000).
[22]
H.M. Soner and N. Touzi, Super-replication under Gamma constraint, Journal on Control and Optimization 39, 73-96 (2000).
[21]
P.-F. Koehl, H. Pham and N. Touzi, On super-replication under Transaction costs in general discrete-time models, Theory of Probability and its Applications 45, 783-788 (1999).
[20]
L. Carassus, H. Pham and N. Touzi, Arbitrage and domination cost in a discrete-time 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, 373-388.

[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, 31-56 (1999).
[17]
N. Touzi, Optimal insurance demand under marked point processes shocks, Annals of Applied Probability 10, 283-312 (2000).
[16]
J. Cvitanic, H. Pham and N. Touzi, Super-replication in stochastic volatility models with portfolio constraints, Journal of Applied Probability 36, 523-545 (1999).
[15]
J. Cvitanic, H. Pham and N. Touzi, A closed-form solution for the problem of super-replication under transaction costs, Finance and Stochastics 3, 35-54 (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, 391-412 (1999).
[12]
P.-F. Koehl, H. Pham and N. Touzi, Hedging in discrete-time  under Transaction costs and continuous-time limit, Journal of Applied Probability 36, 163-178 (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, 411-422 (1999).
[9]
E. Fournié, J. Lebuchoux and N. Touzi, Small Noise Expansion and Importance Sampling, Asymptotic Analysis 14, 361-376 (1997).
[8]
E. Jouini, P.-F. Koehl and N. Touzi, Incomplete Markets, Transaction costs and Liquidity effects, European Journal of Finance 4, 325-348.
[7]
L.P. Hansen, J.A. Scheinkman and N. Touzi, Spectral Methods for Identifying Scalar Diffusions, Journal of Econometrics 86, 1-32.
[6]
J.-P. Florens, E. Renault and N. Touzi, Testing Embeddability by Stationary Reversible Continuous-Time 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, 399-412 (1997).
[2]
H. Pham and N. Touzi, Equilibrium State Prices in a Stochastic Volatility Model, Mathematical Finance 6, 215-236 (1996).

[1] E. Renault and N. Touzi, Option Hedging and Implicit Volatilities, Mathematical Finance 6, 279-302 (1996).