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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
* Third
SMAI-European Summer in Financial Mathematics
* Euro-Mediterranean
School on Mathematical Finance,
* 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).
1.
Deterministic and stochastic control problems related to finance and insurance :
- Convex duality methods in the utility
maximization problem with market imperfection, non-smooth utility function...
- Pricing and hedging by utility
indifference.
- Super-replication and its
extension to the stochastic target problem, duality and direct
characterization.
- Connection with FBSDE’s and geometric flows in the field of
differential geometry.
- Variance reduction methods.
- Malliavin
calculus for the computation of Greeks.
- Malliavin
calculus for optimal stopping problems, i.e. American options.
- BSDEs
and Probabilistic numerical methods for nonlinear PDEs
[75]
[74]
A. Galichon,
P. Henry-Labordère and
marginals, with an
application to Lookback options. (pdf file)
[73]
G.-E. Espinosa and
N. Touzi, Optimal Investment under Relative Performance Concerns. (pdf file)
[72]
X. Tan and
N. Touzi, Optimal Transportation under Controlled Stochastic Dynamics. (pdf file)
[71]
G.-E. Espinosa and
[70]
R. Belaouar,
A. Fahim and N. Touzi, Optimal Production Policy under
Carbon Emission Market. (pdf file)
[69]
R. Carmona, F. Delarue, G.-E. Espinosa and
[68]
M. Soner,
[67]
D. Possamaï,
M. Soner, and N. Touzi, Large liquidity expansion
of superhedging costs, Asymptotic Analysis: Theory,
Methods and Applications, to
appear. (pdf file)
[66]
M. Soner,
[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.
[63]
M. Soner,
[62]
M. Soner,
[61]
R. Aïd,
O. Féron,
[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, to appear. (ps file)
[58]
D. Crisan, K. Manolarakis
and N. Touzi, On the
[57]
B. Bouchard, R. Elie and N. Touzi, Stochastic
Target Problems with Controlled Loss.
[56]
R. Aïd,
L. Campi, A. Nguyen Huu, and
[55]
M. Soner and
[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
[52]
Porchet A.,
[51]
E. Jouini, W. Schachermayer and
[50]
I. Ben Tahar, M. Soner and
[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,
[43]
M. Soner and
[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
[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
[35]
E. Jouini, M. Meddeb and
[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
[31]
H.M. Soner and
[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
[26] H.M. Soner and
[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
[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
[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
[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
[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
[8] E. Jouini, P.-F. Koehl and
[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
[2] H. Pham and N. Touzi, Equilibrium State Prices in a
Stochastic Volatility Model, Mathematical Finance 6, 215-236 (1996).
[1] E. Renault and