
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
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)
Chaînes de Markov et
martingales en temps discret, Ecole
Polytechnique, 2ème année, PA Mathématiques Appliquées (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, Bowen Zheng.
Past: Hadrien De March (June 2018, PostDoc Ecole
Polytechnique)
Gaoyue Guo (October 2016, presently PostDoc Universityof Michigan)
Zhenjie
Ren (October 2015, Assistant Professor
University Paris Dauphine)
Guillaume
Royer (December 2013, Bank of America,
London)
Emilie
Fabre (February 2012 Société Générale,
Paris)
Xiaolu Tan (December 2011, Assistant Professor University Paris Dauphine)
Dylan
Possamaï (December 2011, Assistant
Professor Columbia University)
GillesEdouard
Espinosa (June 2010, BNP Paribas)
Arash
Fahim (April 2010, Associate Professor Florida
State University)
Arnaud
Porchet (February 2008, Goldman Sachs,
London)
Romuald
Elie (December 2006, Professor University
Marne la Vallée)
Fabian
Astic (March 2007, Moody’s NY)
Imen
Ben Tahar (March 2005, Assistant
Professor University Paris Dauphine)
Amina
Zeghal (January 2005, University Dauphine
Tunis)
Moez
Mrad (December 2003, Calyon, London)
Bruno
Bouchard (January 2001, Professor
University Paris Dauphine).
RECENT PAPERS
[111] A. Richard, X. Tan, N. Touzi, On the Root solution to the Skorokhod embedding problem given full
marginals, arXiv:1810.10048
[110] R. Aïd, D. Possamaï, N. Touzi, J. Zhang, Optimal electricity
demand response contracting with responsiveness incentives, arXiv:1810.09063
[109] D. Possamaï, N. Touzi, J. Zhang, Zerosum pathdependent stochastic differential games in weak
formulation, arXiv:1808.03756
[108] Z. Ren, N. Touzi, J. Yang, Nonlinear predictable representation
and L1solutions of secondorder backward SDEs, arXiv:1808.05816
[107] O. El Euch, T. Mastrolia, M.
Rosenbaum, N. Touzi, Optimal maketake
fees for market making regulation, (pdf file).
[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] Z. Ren, N. Touzi, and J. Zhang, Comparison of Viscosity Solutions of
Semilinear PathDependent PDEs, arXiv:1410.7281.
ACCEPTED PAPERS
[103] H. De March, N. Touzi, Irreducible convex paving for
decomposition of multidimensional martingale transport plans, Annals of Probability, to appear. arXiv:1702.08298
[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,
49(5), 40934116 (2017). (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, Volume 46, Number
1 (2018), 126174. (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. Volume
127, Issue 9, Pages 30053013
(September 2017). (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, 127(3):927956 (2017).(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, 63(10):33283346. 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,
11961216 (2016). (pdf file)
[85]
I. Ekren, N. Touzi and J. Zhang, Viscosity Solutions of Fully
Nonlinear Parabolic Path Dependent PDEs: Part II, Annals of Probability, Vol. 44, 4 (2016), 25072553. 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, vol. 40 (11), pp
20052046, 2015. 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. (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, Volume 25,
Issue 2 April 2015, Pages 221–257. (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, Volume 42, Number 1 (2014), 204236. (pdf file)
[70]
G.E. Espinosa and N. Touzi, Detecting
the Maximum of a MeanReverting Scalar Diffusion, SIAM Journal on Control and
Optimization, Vol. 50, No. 5, pp.
2543–2572 (2012). (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, Volume 23, Number 3
(2013), 10861128. (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).