Bruno Bouchard
Professor of Mathematics
Université Paris Dauphine - PSL

Université Paris-Dauphine, Ceremade, bureau C618bis, place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

Lecture notes
Recent papers
Published papers

External Links
Master Masef
Bachelier Seminar


Valorisation des produits dérivés : des théorèmes fondamentaux à la couverture sous contrainte de risque (abstract, erratum)
Economica, série Economie et Statistiques Avancées.

Fundamentals and Advanced Techniques in Derivatives Hedging (abstract)
Springer, Universitext.

Lecture notes

Almost sure hedging under permanent price impact (slides pdf)

Portfolio management under risk contraints (pdf)

Introduction to stochastic control of mixed diffusion processes, viscosity solutions and applications in finance and insurance (pdf)

Mini-course on Stochastic Targets and related problems (slides pdf)

Stochastic Control for Optimal Trading: State of Art and Perspectives (an attempt of) (slides pdf)

Lecture notes on BSDEs - Main existence and stability results (pdf)

Numerical Approximation of BSDEs by using Backward Euler schemes (slides pdf)

Méthodes de Monte-Carlo en Finance (pdf)

Recent papers

(point on the title to see the abstract)

Itô-Dupire’s formula for C0,1-functionals of càdlàg weak Dirichlet processes, (pdf)
with Maximilien Vallet.

Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability, (pdf, slides)
with Grégoire Loeper and Xiaolu Tan.

Diffusive limit approximation of pure-jump optimal stochastic control problems, (pdf)
with Marc Abeille and Lorenzo Croissant.

A C0,1-functional Itô’s formula and its applications in mathematical finance , (pdf,slides)
with Grégoire Loeper and Xiaolu Tan.

Simple Bounds for Transaction Costs, (revised pdf, slides)
with Johannes Muhle-Karbe.

Published/Accepted papers

(point on the title to see the abstract)

Understanding the dual formulation for the hedging of path-dependent options with price impact, (pdf, slides)
with Xiaolu Tan, to appear in Annals of Applied Probability.

A quasi-sure optional decomposition and super-hedging result on the Skorokhod space, (revised pdf)
with Xiaolu Tan, Finance and Stochastics, 25, 505-528, 2021.

Computation of Expected Shortfall by fast detection of worst scenarios, (revised pdf)
with Adil Reghai and Benjamin Virrion, Quantitative Finance, 21(7), 1087-1108, 2021.

Quenched mass transport of particles towards a target, (revised pdf, slides)
with Boualem Djehiche and Idris Kharroubi, JOTA, 186(2), p.28, 2020.

Second order stochastic target problems with generalized market impact, (revised pdf, slides)
with Grégoire Loeper, Mete Soner and Chao Zhou, SIAM Journal on Control and Optimization, 57(6), 4125-4149, 2019.

Optimal inventory management and order book modeling, (revised pdf)
with Nicolas Baradel, David Evangelista and Othmane Mounjid (Cemracs 2017 project), ESAIM: Proceedings and Survey, 65, 145-181, 2019.

Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view, (pdf)
with Ki Wai Chau, Arij Manai and Ahmed Sid-Ali (Cemracs 2017 project), ESAIM: Proceedings and Survey, 65, 294-308, 2019.

Numerical approximation of general Lipschitz BSDEs with branching processes, (pdf)
with Xiaolu Tan, Xavier Warin, ESAIM: Proceedings and Survey, 65, 309-329, 2019.

Stochastic invariance of closed sets with non-Lipschitz coefficients, (pdf, slides)
with Eduardo Abi Jaber and Camille Illand, Stochastic Processes and their Applications, 129(5), 1726-1748, 2019.

Super-replication with proportional transaction cost under model uncertainty, (pdf)
with Shuoqing Deng and Xiaolu Tan, Mathematical Finance, 29(3), 837-860, 2019.

Equilibrium Returns with Transaction Costs, (pdf)
with Masaaki Fukasawa, Martin Herdegen and Johannes Muhle-Karbe, Finance and Stochastics, 22(3), 569-601, 2018.

Optimal control under uncertainty and Bayesian parameters adjustments, (revised pdf)
with Nicolas Baradel and Ngoc Minh Dang, SIAM Journal on Control and Optimization, 56(2), 1038-1057, 2018.

A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, (revised pdf, slides)
with Dylan Possamai, Xiaolu Tan and Chao Zhou, Annales de l'Institut Henri Poincaré B, 54(1), 154-172, 2018.

Regularity of BSDEs with a convex constraint on the gains-process, (pdf)
with Romuald Elie and Ludovic Moreau, Bernoulli, 24(3), 1613-1635, 2018.

Numerical approximation of BSDEs using local polynomial drivers and branching processes, (revised pdf)
with Xiaolu Tan, Xavier Warin and Yiyi Zou, Monte Carlo Methods and Applications, 23(4), 241-264, 2017.

Hedging of covered options with linear price impact and gamma constraint, (pdf,slides)
with Grégroire Loeper and Yiyi Zou, SIAM Journal on Control and Optimization, 55(5), 3319-3348, 2017.

First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations, (revised pdf, slides)
with Stefan Geiss and Emmanuel Gobet, Bernoulli, 23(3), 1631-1662, 2017.

Robust Fundamental Theorem for Continuous Processes, (pdf, slides)
with Sara Biagini, Constantinos Kardaras and Marcel Nutz, Mathematical Finance, 27(4), 963-987, 2017.

Optimal trading with online parameters revisions, (pdf)
with Nicolas Baradel and Ngoc Minh Dang, Market Microstructure and Liquidity, 2(03n04), 2016.

A general Doob-Meyer-Mertens decomposition for g-supermartingale systems, (revised pdf, slides)
with Dylan Possamai and Xiaolu Tan, Electronic Journal of Probability, 21, 2016.

Hedging under an expected loss constraint with small transaction costs, (revised pdf)
with Ludovic Moreau and Mete Soner, SIAM Journal on Financial Mathematics, 7(1), 508-551, 2016.

A backward dual representation for the quantile hedging of Bermudean options, (pdf)
with Géraldine Bouveret and Jean-François Chassagneux, SIAM Journal on Financial Mathematics, 7(1), 215-235, 2016.

Almost-sure hedging with permanent price impact, (pdf, slides)
with Grégoire Loeper and Yiyi Zou, Finance and Stochastics, 20(3), 741-771, 2016.

Consistent Price Systems under Model Uncertainty, (revised pdf, slides)
with Marcel Nutz, Finance and Stochastics, 20(1), 83-98, 2016.

Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions, (revised pdf, slides)
with Marcel Nutz, Mathematics of Operations Research, 2016, 41(1), 109-124.

Arbitrage and duality in nondominated discrete-time models, (pdf, slides)
with Marcel Nutz, Annals of Applied Probability, 2015, 25(2), 823-859.

BSDEs with weak terminal condition, (pdf, slides)
with Romuald Elie and Anthony Réveillac, Annals of Probability, 2015, 43(2), 572-604.

Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs, (pdf)
with Emmanuel Lépinette and Erik Taflin, Stochastic Processes and their Applications, 2014, 124, 3231-3259.

Stochastic Target Games with Controlled Loss, (pdf, slides)
with Ludovic Moreau and Marcel Nutz, Annals of Applied Probability, 2014, 24(3), 899-934.

No-arbitrage of second kind in countable markets with proportional transaction costs, (pdf)
with Erik Taflin, Annals of Applied Probability, 2013, 23(2), 427-454.

Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation,
with Ngoc Minh Dang,
Finance & Stochastics, 2013, 17(1), 31-72 (slides).

No marginal arbitrage of the second kind for high production regimes in discrete time production-investment models with proportional transaction costs,
with Adrien Nguyen Huu, Mathematical Finance, 2013, 23(2), 366-386.

Weak Dynamic Programming for Generalized State Constraints, (revised pdf, slides)
with Marcel Nutz, SIAM Journal on Control and Optimization, 2012, 50(6), 3344-3373.

A note on utility based pricing and asymptotic risk diversification, (pdf)
with Romuald Elie and Ludovic Moreau, Mathematics and Financial Economics, 2012, 6(1), 59-74.

A stochastic target approach for P&L matching problems,
with Vu Than Nam, Mathematics of Operation Research, 2012, 37(3), 526-558 (pdf).

Optimal Control vs Stochastic Target problems: An Equivalence Result,
with Ngoc Minh Dang, Systems & Control Letters, 2012, 61 (2), 343-346.

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.

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.

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.

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.

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.

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.

Strong Approximations of BSDEs in a domain, (slides)
with Stéphane Menozzi, Bernoulli , 2009, 15 (4), 1117-1147.

Transaction costs in financial models,
with Elyes Jouini, Encyclopedia of Quantitative Finance, Rama Cont (Ed), Wiley.

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.

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).

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).

No-arbitrage in discrete-time markets with proportional transaction costs and general information structure,
Finance and Stochastics, 2006, 10 (2), 276-297 (slides).

Barrier option hedging under constraints: a viscosity approach,
with Imen Bentahar, SIAM Journal on Control and Optimization , 2006, 45 (5), 1846-1874.

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.

Maturity randomization for stochastic control problems,
with Nicole El Karoui and Nizar Touzi, Annals of Applied Probability, 2005, 15 (4), 2575-2605.

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.

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.

Wealth-Path Dependent Utility Maximization in Incomplete Markets,
with Huyen Pham, Finance and Stochastics, 2004, 8 (4), 579-603.

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.

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.

Stochastic Target with Mixed diffusion processes,
Stochastic Processes and their Applications, 2002, 101, 273-302.

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.

Explicit Solution of the Multivariate Super-Replication Problem under Transaction Costs,
with Nizar Touzi, Annals of Applied Probability, 2000, 10, 685-708.


(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.