CEREMADE
Bouchard Bruno
Professeur des universités
Biographie
Bruno Bouchard est Professeur de mathématiques à l’Université Paris Dauphine - PSL. Après des études d’économie et de finance, il a obtenu un doctorat en mathématiques appliquées et s’est spécialisé dans les aspects mathématiques de la gestion des risques. Il a dirigé la spécialité recherche de master Masef et dirige actuellement le diplôme de formation professionnelle DifiQ, spécialisés en finance quantitative. Il a été ou est encore membre du committee meeting de la Bachelier Finance Society et Editeur Associé des revues Finance and Stochastics, Mathematical Finance, JOTAet de SIAM Journal on Financial Mathematics. Ses travaux couvrent un spectre large qui porte sur l’évaluation d’actif en marchés imparfaits, l’analyse des méthodes numériques probabilistes, le contrôle optimal stochastique et la modélisation de problématiques de gestion concrètes en collaboration avec l’industrie.
Il est actuellement Président de l'Université Paris Dauphine - PSL.
Publications
Articles
Bouchard B., Tan X., Wang J. (2024), A C1-Itô's formula for flows of semimartingale distributions, Applied Mathematics and Optimization, vol. 90, n°1
Abeille M., Bouchard B., Croissant L. (2023), Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems, Journal of Optimization Theory and Applications, vol. 196, n°1, p. 147-176
Bouchard B., Loeper G., Tan X. (2023), Approximate viscosity solutions of path-dependent PDEs and Dupire's vertical differentiability, Annals of Applied Probability, vol. 33, n°6B, p. 5781-5809
Bouchard B., Loeper G., Tan X. (2022), A C0,1-functional Itô's formula and its applications in mathematical finance, Stochastic Processes and their Applications, vol. 148, p. 299-323
Bouchard B., Tan X. (2022), Understanding the dual formulation for the hedging of path-dependent options with price impact, Annals of Applied Probability, vol. 32, n°3, p. 1705-1733
Bouchard B., Muhle-Karbe J. (2022), Simple bounds for utility maximization with small transaction costs, Stochastic Processes and their Applications, vol. 146, p. 98-113
Bouchard B., Tan X. (2021), A quasi-sure optional decomposition and super-hedging result on the Skorokhod space, Finance and Stochastics, n°25, p. 505–528
Bouchard B., Reghai A., Virrion B. (2021), Computation of Expected Shortfall by fast detection of worst scenarios, Quantitative Finance, vol. 21, n°7, p. 1087-1108
Bouchard B., Djehiche B., Kharroubi I. (2020), Quenched mass transport of particles towards a target, Journal of Optimization Theory and Applications, vol. 186, n°2, p. 28
Bouchard B., Chau K., Manai A., Sid-Ali A. (2019), Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view, ESAIM: Proceedings and Surveys, vol. 65, p. 294-308
Bouchard B., Deng S., Tan X. (2019), Superreplication with proportional transaction cost under model uncertainty, Mathematical Finance, vol. 29, n°3, p. 837-860
Baradel N., Bouchard B., Evangelista D., Mounjid O. (2019), Optimal inventory management and order book modeling, ESAIM: Proceedings and Surveys, vol. 65, p. 145-181
Bouchard B., Tan X., Warin X. (2019), Numerical approximation of general Lipschitz BSDEs with branching processes, ESAIM: Proceedings and Surveys, vol. 65, p. 309-329
Bouchard B., Loeper G., Soner M., Zhou C. (2019), Second order stochastic target problems with generalized market impact, SIAM Journal on Control and Optimization, vol. 57, n°6, p. 4125-4149
Abi Jaber E., Bouchard B., Illand C. (2019), Stochastic invariance of closed sets with non-Lipschitz coefficients, Stochastic Processes and their Applications, vol. 129, n°5, p. 1726-1748
Bouchard B., Possamaï D., Tan X., Zhou C. (2018), A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, Annales Henri Poincaré, vol. 54, n°1, p. 154-172
Bouchard B., Fukasawa M., Herdegen M., Muhle-Karbe J. (2018), Equilibrium returns with transaction costs, Finance and Stochastics, vol. 22, n°3, p. 569-601
Bouchard B., Elie R., Moreau L. (2018), Regularity of BSDEs with a convex constraint on the gains-process, Bernoulli, vol. 24, n°3, p. 1613-1635
Baradel N., Bouchard B., Dang N. (2018), Optimal Control Under Uncertainty and Bayesian Parameters Adjustments, SIAM Journal on Control and Optimization, vol. 56, n°2, p. 1038-1057
Bouchard B., Geiss S., Gobet E. (2017), First time to exit of a continuous Itô process: General moment estimates and L1 -convergence rate for discrete time approximations, Bernoulli, vol. 23, n°3, p. 1631-1662
Bouchard B., Loeper G., Zou Y. (2017), Hedging of covered options with linear market impact and gamma constraint, SIAM Journal on Control and Optimization, vol. 55, n°5, p. 3319–3348
Biagini S., Bouchard B., Kardaras C., Nutz M. (2017), Robust Fundamental Theorem for Continuous Processes, Mathematical Finance, vol. 27, n°4, p. 963-987
Roumiguié A., Sigel G., Poilvé H., Bouchard B., Vrieling A., Jacquin A. (2017), Insuring forage through satellites: testing alternative indices against grassland production estimates for France, International Journal of Remote Sensing, vol. 38, n°7, p. 1912-1939
Bouchard B., Tan X., Warin X., Zou Y. (2017), Numerical approximation of BSDEs using local polynomial drivers and branching processes, Monte Carlo Methods and Applications, vol. 23, n°4, p. 241-263
Bouchard B., Possamaï D., Tan X. (2016), A general Doob-Meyer-Mertens decomposition for g-supermartingale systems, Electronic Journal of Probability, vol. 21, p. 21
Bouchard B., Moreau L., Soner M. (2016), Hedging under an expected loss constraint with small transaction costs, SIAM Journal on Financial Mathematics, vol. 7, n°1, p. 508-551
Bouchard B., Loeper G., Zou Y. (2016), Almost-sure hedging with permanent price impact, Finance and Stochastics, vol. 20, n°3, p. 741-771
Baradel N., Bouchard B., Dang N. (2016), Optimal trading with online parameters revisions, Market Microstructure and Liquidity, vol. 2, n°03n04, p. 27
Bouchard B., Nutz M. (2016), Consistent Price Systems under Model Uncertainty, Finance and Stochastics, vol. 20, n°1, p. 83-98
Bouchard B., Bouveret G., Chassagneux J-F. (2016), A Backward Dual Representation for the Quantile Hedging of Bermudan Options, SIAM Journal on Financial Mathematics, vol. 7, n°1, p. 215-235
Bouchard B., Elie R., Réveillac A. (2015), BSDEs with weak terminal condition, Annals of Probability, vol. 43, n°2, p. 572-604
Bouchard B., Nutz M. (2015), Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions, Mathematics of Operations Research, vol. 41, n°1, p. 109-124
Bouchard B., Nutz M. (2015), Arbitrage and Duality in Nondominated Discrete-Time Models, Annals of Applied Probability, vol. 25, n°2, p. 823-859
Bouchard B., Moreau L., Nutz M. (2014), Stochastic Target Games with Controlled Loss, Annals of Applied Probability, vol. 24, n°3, p. 899-934
Bouchard B., Lépinette-Denis E., Taflin E. (2014), Robust no-free lunch with vanishing risk, a continuum of assets and proportional transaction costs, Stochastic Processes and their Applications, vol. 124, n°10, p. 3231–3259
Bouchard B., Nguyen Huu A. (2013), No marginal arbitrage of the second kind for high production regimes in discrete time production-investment models with proportional transaction costs, Mathematical Finance, vol. 23, n°2, p. 366-386
Bouchard B., Taflin E. (2013), No-arbitrage of second kind in countable markets with proportional transaction costs, Annals of Applied Probability, vol. 23, n°2, p. 427-454
Bouchard B., Dang N. (2013), Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation, Finance and Stochastics, vol. 17, n°1, p. 31-72
Bouchard B., Nutz M. (2012), Weak Dynamic Programming for Generalized State Constraints, SIAM Journal on Control and Optimization, vol. 50, n°6, p. 3344-3373
Bouchard B., Elie R., Moreau L. (2012), A note on utility based pricing and asymptotic risk diversification, Mathematics and Financial Economics, vol. 6, n°1, p. 59-74
Bouchard B., Dang N. (2012), Optimal Control versus Stochastic Target problems: An Equivalence Result, Systems & Control Letters, vol. 61, n°2, p. 343-346
Bouchard B., Vu T. (2012), A stochastic target approach for P&L matching problems, Mathematics of Operations Research, vol. 37, n°3, p. 526-558
Bouchard B., Dang N., Lehalle C-A. (2011), Optimal Control of Trading Algorithms: A General Impulse Control Approach, SIAM Journal on Financial Mathematics, vol. 2, n°1, p. 404-438
Bouchard B., Touzi N. (2011), Weak Dynamic Programming Principle for Viscosity Solutions, SIAM Journal on Control and Optimization, vol. 49, n°3
Bouchard B., Vu T. (2010), The obstacle version of the Geometric Dynamic Programming Principle: Application to the pricing of American options under constraints, Applied Mathematics and Optimization, vol. 61, n°2, p. 235-265
Bouchard B., Elie R., Imbert C. (2010), Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol. 48, n°5, p. 3501-3531
Bouchard B., Elie R., Touzi N. (2009), Stochastic target problems with controlled loss, SIAM Journal on Control and Optimization, vol. 48, n°5, p. 3123-3150
Bouchard B., Menozzi S. (2009), Strong Approximations of BSDEs in a domain, Bernoulli, vol. 15, n°4, p. 1117-1147
Bouchard B., Chassagneux J-F. (2009), Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs, Electronic Journal of Probability, vol. 14, n°paper numéro 24, p. 612-632
Bouchard B. (2009), A stochastic target formulation for optimal switching problems in finite horizon, Stochastics: An International Journal of Probability and Stochastic Processes , vol. 81, n°2, p. 171 - 197
Bouchard B. (2008), Optimal reflection of diffusions and barrier options pricing under constraints, SIAM Journal on Control and Optimization, vol. 47, n°4, p. 1785–1813
Bouchard B., Elie R. (2008), Discrete-time approximation of decoupled Forward–Backward SDE with jumps, Stochastic Processes and their Applications, vol. 118, n°1, p. 53-75
Bouchard B., Chassagneux J-F. (2008), Discrete time approximation for continuously and discretely reflected BSDE's, Stochastic Processes and their Applications, vol. 118, n°12, p. 2269-2293
Ben Tahar I., Bouchard B. (2007), Explicit characterization of the super-replication strategy in financial markets with partial transaction costs, Stochastic Processes and their Applications, vol. 117, n°5, p. 655-672
Bouchard B. (2006), No-arbitrage in discrete-time markets with proportional transaction costs and general information structure, Finance and Stochastics, vol. 10, n°2, p. 276-297
Ben Tahar I., Bouchard B. (2006), Barrier option hedging under constraints: a viscosity approach, SIAM Journal on Control and Optimization, vol. 45, n°5, p. 1846-1874
Bouchard B. (2005), A version of the G-conditionial bipolar theorem in L0(Rd;P), Journal of Theoretical Probability, vol. 18, n°2, p. 439-467
Bouchard B., Pham H. (2005), Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns, Annals of Applied Probability, vol. 15, n°4, p. 2393-2421
Bouchard B., Temam E. (2005), On the Hedging of American Options in Discrete Time Markets with Proportional Transaction Costs, Electronic Journal of Probability, vol. 10, n°22, p. 746-760
Bouchard B., Karoui N., Touzi N. (2005), Maturity randomization for stochastic control problems, Annals of Applied Probability, vol. 15, n°4, p. 2575-2605
Bouchard B., Pham H. (2004), Wealth-Path Dependent Utility Maximization in Incomplete Markets, Finance and Stochastics, vol. 8, n°4, p. 579-603
Bouchard B., Ekeland I., Touzi N. (2004), On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance and Stochastics, vol. 8, n°1, p. 45-71
Bouchard B., Zhegal A., Touzi N. (2004), Dual Formulation of the Utility Maximization Problem : the case of Nonsmooth Utility, Annals of Applied Probability, vol. 14, n°2, p. 678-717
Bouchard B., Touzi N. (2004), Discrete-Time Approximation and Monte-Carlo Simulation of Backward Stochastic Differential Equations, Stochastic Processes and their Applications, vol. 111, n°2, p. 175-206
Bouchard B., Mazliak L. (2003), A multidimensional bipolar theorem in L0(Rd;P), Stochastic Processes and their Applications, vol. 107, n°2, p. 213-231
Bouchard B. (2002), Stochastic Target with Mixed diffusion processes, Stochastic Processes and their Applications, vol. 101, n°2, p. 273-302
Bouchard B. (2002), Utility Maximization on the Real Line under Proportional Transaction Costs, Finance and Stochastics, vol. 6, n°4, p. 495-516
Bouchard B., Kabanov Y., Touzi N. (2001), Option pricing by large risk aversion utility under transaction costs, Decisions in Economics and Finance, vol. 24, n°2, p. 127-136
Bouchard B., Touzi N. (2000), Explicit solution to the multivariate super-replication problem under transaction costs, Annals of Applied Probability, vol. 10, n°3, p. 685-708
Ouvrages
Bouchard B., Chassagneux J-F. (2016), Fundamentals and Advanced Techniques in Derivatives Hedging, Berlin Heidelberg: Springer, 280 p.
Bouchard B., Chassagneux J-F. (2014), Valorisation des produits dérivés: des théorèmes fondamentaux à la couverture sous contrainte de risque Economica, 304 p.
Chapitres d'ouvrage
Bouchard B., Warin X. (2012), Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods, in Oudjane, Nadia, Numerical Methods in Finance, Berlin: Springer, p. 215-255
Bouchard B., Jouini E. (2010), Transaction costs in financial model, in Cont, Rama, Encyclopedia of Quantitative Finance Wiley, p. 1976
Bouchard B., Elie R., Touzi N. (2009), Discrete-Time Approximation of BSDEs and Probabilistic Schemes for Fully Nonlinear PDEs, in Schachermayer, Walter, Advanced Financial Modelling Radon Series on Computational and Applied Mathematics, p. 91-124
Directions d'ouvrage
Bouchard B., Chafaï D. (2021), Covid-19 | Regards croisés sur la crise, Paris: Université Paris-Dauphine, 113 p.
Communications avec actes
Croissant L., Abeille M., Bouchard B. (2024), Near-continuous time Reinforcement Learning for continuous state-action spaces, in Claire Vernade, Daniel Hsu, Proceedings of Machine Learning Research (PMLR), 444-498 p.
Fieuzal R., Roumiguie A., Fradin J., Bouchard B., Ceschia E. (2020), Validation of the Grassland Production Index, an Insurance Product Estimated at the National Scale, on a Dense Experimental Device, in , Piscataway, NJ, IEEE - Institute of Electrical and Electronics Engineers
Prépublications / Cahiers de recherche
Bouchard B., Tan X. (2023), On the regularity of solutions of some linear parabolic path-dependent PDEs, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 33 p.
Bouchard B., Vallet M. (2021), Itô-Dupire's formula for C^{0,1}-functionals of càdlàg weak Dirichlet processes, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 15 p.
Bouchard B., Cheridito P., Hu Y. (2018), BSDE formulation of combined regular and singular stochastic control problems, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 11 p.