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Nizar Touzi Professor, Applied Mathematics |
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Centre de
Mathématiques Appliquées Ecole Polytechnique UMR CNRS 7641 91128 Palaiseau Cedex FRANCE |
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Téléphone: |
33 (0)1-69-33-46-12 |
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Fax: |
33 (0)1-69-33-30-11 |
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e-mail: |
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, April-June 2010 (pdf file).
-
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
[84]
P. Henry-Labordère
and N. Touzi, An Explicit Martingale Version of Brenier's Theorem. (pdf
file)
[83]
P. Henry-Labordère,
X. Tan and N. Touzi, A numerical algorithm for a class of BSDE via branching
process.
arXiv:1302.4624 [math.NA](pdf
file)
[82]
D. Possamaï, G. Royer
and N. Touzi, On the robust superhedging of measurable claims. arXiv:
1302.1850v2. (pdf file)
[81]
D. Possamaï, N. Touzi
and M. Soner, Homogenization and asymptotics for small transaction costs:
the multidimensional case. arXiv:1212.6275
[80]
I. Ekren, N. Touzi and J.
Zhang, Viscosity Solutions of Fully Nonlinear
Parabolic Path Dependent PDEs: Part II, arXiv:1210.0007v2[math.PR].
[79]
I. Ekren, N. Touzi and J.
Zhang, Viscosity Solutions of Fully Nonlinear
Parabolic Path Dependent PDEs: Part I, arXiv:1210.0006v2[math.PR].
[78]
I. Ekren, N. Touzi and J.
Zhang, Optimal Stopping under Nonlinear Expectation, arXiv:1209.6601v2[math.PR].
[77]
J. Obloj, P.
Henry-Labordère, P. Spoida, and N. Touzi, Maximum Maximum of
Martingales given Marginals. (pdf
file)
[76]
R. Belaouar, A. Fahim and
N. Touzi, Optimal Production Policy under Carbon Emission Market. (pdf file)
[75]
M. Soner and N. Touzi, Homogenization
and asymptotics for small transaction costs. SIAM Journal on Control and Optimization, to appear (pdf
file)
[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, to
appear. (pdf file)
[73]
G.-E. Espinosa and
N. Touzi, Optimal Investment under Relative Performance Concerns. Mathematical
Finance, to appear. (pdf
file)
[72]
X. Tan and
N. Touzi, Optimal Transportation under Controlled Stochastic Dynamics, Annals
of Probability, to appear. (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.
[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.
[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.
[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.
[44]
M. Mrad, N. Touzi, and A. Zeghal, Monte Carlo
estimation of a joint density using Malliavin calculus.
[43]
M. Soner and N. Touzi, Hedging under gamma
constraints by optimal stopping and face-lifting.
[42]
R. Carmona and N. Touzi, Optimal multiple stopping
and valuation of swing options.
[41]
B. Bouchard, N. El Karoui and N. Touzi, Maturity
randomisation for stochastic control problems.
[40]
P. Cheridito, M. Soner and N. Touzi, Small time
path behavior of double stochastic integrals and applications to stochastic
control.
[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).
[35]
E. Jouini, M. Meddeb and N. Touzi, Vector-valued
measure of risk, Finance and Stochastics, 8, 531-552.
[34]
B. Bouchard, N. Touzi and A. Zeghal, Dual
Formulation of the Utility Maximization Problem : the case of Nonsmooth Utility.
[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.
[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).
[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.
[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).