CEREMADE

## Bouchard Bruno

Full Professor

### Biography

Bruno Bouchard is Professor of Mathematics. After studying economics and finance, he obtained a PhD in applied mathematics, specializing in the mathematical. He headed the the Masef master's research speciality and currently heads the DifiQ professional training diploma, specializing in quantitative finance. He is a member of the committee meeting of the Bachelier Finance Society and Associate Editor of Finance and Stochastics, Mathematical Finance and the SIAM Journal on Financial Mathematics. His work covers a wide spectrum, from asset pricing in imperfect markets analysis of probabilistic numerical methods, stochastic optimal stochastic optimal control and the modeling of concrete management management problems in collaboration with industry.

He is currently Vice-President of the Scientific Council, in charge of research.

### Publications

#### Articles

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

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., 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., 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., 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., 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., 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., 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., 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., Elie R., Moreau L. (2018), Regularity of BSDEs with a convex constraint on the gains-process, Bernoulli, vol. 24, n°3, p. 1613-1635

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

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., 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., 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

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., 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

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., 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

Bouchard B., Nutz M. (2016), Consistent Price Systems under Model Uncertainty, Finance and Stochastics, vol. 20, n°1, p. 83-98

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. (2015), Arbitrage and Duality in Nondominated Discrete-Time Models, Annals of Applied Probability, vol. 25, n°2, p. 823-859

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., 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., 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., 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. (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., 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., 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. (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., 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. (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

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. (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

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

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.