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Lecture notes
Méthodes
de Monte Carlo en Finance (pdf)
Introduction
à l'évaluation d'actifs financiers par absence
d'opportunité d'arbitrage (pdf)
Portfolio management under risk contraints (pdf)
Introduction to stochastic control of mixed diffusion processes, viscosity solutions
and applications in finance and insurance (pdf)
Recent papers
(point on the title to see
the
abstract)
A stochastic target approach for P&L matching problems,
(pdf)
with Vu Than Nam.
Weak Dynamic Programming for Generalized State Constraints,
(pdf, slides)
with Marcel Nutz.
Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application
in optimal book liquidation,
(revised pdf, slides)
with Ngoc Minh Dang.
Published or accepted papers
(point on the title to see
the
abstract)
Duality in Mathematical Finance
A note on utility based pricing and asymptotic risk diversification,
(pdf)
with Romuald Elie and Ludovic Moreau, to appear in Mathematics and Financial Economics.
No-arbitrage of second kind in countable markets with proportional transaction costs,
(pdf)
with Erik Taflin, to appear in Annals of Applied Probability.
No marginal arbitrage of the second kind for high production regimes in
discrete time production-investment models with proportional
transaction costs,
(revised pdf, slides)
with Adrien Nguyen Huu, to appear in Mathematical Finance.
Representation
of continuous linear forms on the set of ladlag processes and the
pricing of American claims under proportional costs,
with Jean-Francois
Chassagneux, Electronic Journal of Probability, 2009, 14, 612-632.
Transaction costs in financial models,
with Elyes Jouini, Encyclopedia of Quantitative Finance, Rama Cont (Ed), Wiley.
No-arbitrage in
discrete-time markets with proportional transaction costs and general
information structure,
Finance
and Stochastics, 2006, 10 (2), 276-297 (slides).
On the Hedging of
American Options in Discrete Time Markets with Proportional Transaction
Costs,
with Emmanuel
Temam, Electronic Journal of Probability,
2005, 10, 746-760.
Optimal consumption in
discrete time financial models with industrial investment opportunities
and non-linear returns,
with
Huyen Pham, Annals
of Applied
Probability, 2005, 15 (4), 2393-2421 (slides).
A version of the G-conditionial bipolar theorem
in L0(Rd;P),
Journal
of Theoretical Probability, 2005, 18 (2), 439 - 467.
Wealth-Path Dependent
Utility Maximization in Incomplete Markets,
with Huyen Pham, Finance and
Stochastics, 2004, 8 (4), 579-603.
Dual Formulation of the
Utility Maximization Problem : the case of Nonsmooth Utility,
with Nizar Touzi and Amina Zeghal, Annals of Applied
Probability, 2004, 14 (2), 678-717.
A multidimensional bipolar
theorem in L0(Rd;P),
with Laurent Mazliak, Stochastic
Processes and their Applications, 2003, 107 (2), 213-231.
Utility Maximization on
the Real Line under Proportional Transaction Costs,
Finance
and Stochastics, 2002, 6 (4), 495-516.
Option pricing by large
risk aversion utility under transaction costs,
with Youri Kabanov and Nizar Touzi, Decisions
in Economics and Finance, 2001, 24, 127-136.
Optimal Control and Applications in Finance
Optimal Control vs Stochastic Target problems: An Equivalence Result,
(pdf)
with Ngoc Minh Dang, Systems & Control Letters, 2012, 61 (2), 343-346.
Optimal control of trading algorithms: a general impulse control approach,
with Ngoc Minh Dang et Charles-Albert Lehalle, SIAM Journal on Financial Mathematics, 2011, 4, 404-438.
Weak Dynamic Programming Principle for Viscosity Solutions,
(PDF, slides)
with Nizar Touzi, SIAM Journal on Control and Optimization, 2011, 49 (3), 948-962.
Optimal Control under Stochastic Target Constraints,
(pdf, slides)
with Romuald Elie and Cyril Imbert, SIAM Journal on Control and Optimization, 2010, 48 (5), 3501-3531.
Stochastic target problems with controlled loss,
(pdf, slides)
with Romual Elie and Nizar Touzi, SIAM Journal on Control and Optimization, 2009, 48 (5), 3123-3150.
The obstacle version of the Geometric Dynamic Programming Principle:
Application to the pricing of American options under constraints,
with Than Nam Vu, Applied Mathematics and Optimization, 2010, 61 (2), 235-265.
A stochastic target
formulation for optimal switching problems in finite horizon.
Stochastics, 2009, 81 (2), 171-197.
Optimal reflection of
diffusions and barrier options pricing under constraints,
(slides).
SIAM Journal on Control and Optimization, 2008, 47 (4), 1785-1813.
Barrier option hedging
under constraints: a viscosity approach,
with Imen Bentahar,
SIAM Journal on Control
and Optimization , 2006, 45 (5), 1846-1874.
Explicit
characterization of the super-replication strategy in financial markets
with partial transaction costs,
with
Imen Bentahar, Stochastic
Processes and their Applications, 2007, 117 (5), 655-672.
(slides).
Stochastic Target with
Mixed diffusion processes,
Stochastic
Processes and their Applications, 2002, 101, 273-302.
Explicit Solution of the
Multivariate Super-Replication Problem under Transaction Costs,
with Nizar Touzi, Annals of Applied
Probability, 2000, 10, 685-708.
Numerical Probability
Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods,
(revised pdf)
with Xavier Warin, to appear in Numerical Methods in Finance , Springer Proceedings in Mathematics, ed. R. Carmona, P. Del Moral, P. Hu and N. Oudjane , 2011.
Discrete-Time Approximation of BSDEs and Probabilistic Schemes for Fully Nonlinear PDEs
with Romuald Elie and Nizar Touzi, Radon Series Comp. Appl. Math., Advanced Financial Modelling,
Ed. H. Albrecher, W. Runggaldier and W. Schachermayer, 2009.
Strong Approximations of
BSDEs in a domain, (slides)
with Stéphane
Menozzi, Bernoulli , 2009, 15 (4), 1117-1147.
Discrete time
approximation for continuously and discretely reflected BSDE's,
( slides)
with
Jean-Francois Chassagneux,
Stochastic Processes and their Applications , 2008, 118, 2269-2293.
Discrete time
approximation of decoupled Forward-Backward SDE with jumps,
with Romuald Elie,
Stochastic Processes and their Applications
, 2008, 118 (1), 53-75. (slides).
Maturity randomization
for stochastic control problems,
with
Nicole El Karoui and Nizar Touzi, Annals of Applied
Probability, 2005, 15 (4), 2575-2605.
Discrete-Time
Approximation and Monte-Carlo Simulation of Backward Stochastic
Differential Equations,
with
Nizar Touzi, Stochastic
Processes and their Applications, 2004, 111 (2), 175-206.
On the Malliavin
approach to Monte Carlo approximation of conditional expectations ,
with Nizar Touzi and Ivar Ekeland, Finance and
Stochastics, 2004, 8 (1), 45-71.
Others
(point on the title to see
the
abstract)
Option Pricing via
Utility Maximization in the presence of Transaction Costs : an
Asymptotic Analysis,
Ceremade, 1999.
A Note on the Utility
Based Option Pricing with Proportional Transaction Costs under Large
Risk Aversion,
Crest, 2000.
Exponential hedging and
pricing under proportional transaction costs,
Crest, 2000.
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