Emmanuel GOBET - Research

"Mathscinet Author Profile"

PAPERS

  1. Study of new rare event simulation schemes and their application to extreme scenario generation.
    With A. Agarwal, S. De Marco and G. Liu.
    Mathematics and Computers in Simulation, 2017.
    Preprint available on hal-01249625.
  2. Perturbation of Ornstein-Uhlenbeck stationary distributions: expansion and simulation.
    With Q. She.
    In revision for ESAIM Probability and Statistics, 2017.
    Preprint available on hal-01345926.
  3. Optimal discretization of stochastic integrals for degenerate semimartingale.
    With U. Stazhynski.
    To appear in Annales de l'Institut Henri Poincaré, Probabilités et Statistique, 2017.
  4. Analytical approximations of local-Heston volatility model and error analysis.
    With R. Bompis.
    To appear in Mathematical Finance.
    Preprint available on HAL.
  5. MCMC design-based non-parametric regression for rare-event. Application to nested risk computations
    With G. Fort and E. Moulines.
    Monte Carlo Methods and Applications, Vol. 23(1), pp. 21-42, 2017.
  6. A non-intrusive stratified resampler for regression Monte Carlo: application to solving non-linear equations.
    With G. Liu and J. Zubelli.
    To appear in SIAM Journal on Numerical Analysis, 2017.
    Preprint available on hal-01291056.
  7. Stratified regression Monte-Carlo scheme for semilinear PDEs and BSDEs with large scale parallelization on GPUs.
    With J. Lopez-Salas, P. Turkedjiev, C. Vasquez.
    To appear in SIAM Journal on Scientific Computing, Vol. 38(6), C652-C677, 2017.
    Preprint available on HAL.
  8. Parameter estimation of Ornstein-Uhlenbeck process generating a stochastic graph.
    With G. Matulewicz.
    Statistical Inference for Stochastic Processes, Vol. 20(2), pp. 211-235, 2017.
    Preprint available on hal-01271994.
  9. Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations.
    With P. Turkedjiev.
    Stochastic Processes and their applications, Vol. 127(4), pp. 1171-1203, 2017.
    Preprint available on HAL.
  10. Analytical approximation of Variable Annuities for small volatility and small withdrawal.
    With T. Ben Zineb.
    Theory of Probability and its Applications, Vol. 61(1), pp. 40-56, 2017.
  11. First time to exit of a continuous Ito process: general moment estimates and L1-convergence rate for discrete time approximations.
    With B. Bouchard and S. Geiss.
    Bernoulli, Vol. 23(3), pp. 1631-1662, 2017.
    Preprint available on HAL.
  12. Strong approximation of stochastic processes at random times and application to their exact simulation.
    With M. Mrad.
    Stochastics, 2016.
  13. Empirical Regression Method for Backward Doubly Stochastic Differential Equations.
    With A. Bachouch, A. Matoussi.
    SIAM ASA Journal on Uncertainty Quantification, Vol. 4(1), pp.358-379, 2016.
    Preprint available on HAL.
  14. Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions.
    With P. Turkedjiev.
    Mathematics of Computations, Vol. 85(299), pp.1359-1391, 2016.
    Preprint available on HAL.
  15. Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression.
    With P. Turkedjiev.
    Bernoulli, Vol. 22(1), pp.530-562, 2016.
    Preprint available on HAL.
  16. Analytical approximations of BSDEs with non-smooth driver.
    With S. Pagliarani.
    SIAM Journal on Financial Mathematics, Vol.6, pp.919-958, 2015.
    Preprint available on HAL.
  17. Rare event simulation using reversible shaking transformations.
    With G. Liu.
    SIAM Journal on Scientific Computing, Vol.37(5), pp.A2295-A2316, 2015.
    Preprint available on HAL.
  18. Stochastic Approximation Finite Element method: analytical formulas for multidimensional diffusion process
    With R. Bompis.
    SIAM Journal on Numerical Analysis, Vol.52(6), pp.3140-3164, 2014.
    Preprint available on HAL.
  19. Optimization of joint p-variations of Brownian semimartingales.
    With N. Landon.
    Electronic Communications in Probability, Vol.19(36), 2014.
  20. Fractional smoothness of functionals of diffusion processes under a change of measure.
    With S. Geiss.
    Electronic Communications in Probability, Vol.19(35), 2014.
    Preprint available on arXiv.
  21. Expansion formulas for Best-Of Option on Equity and Inflation.
    With J. Hok.
    International Journal of Theoretical and Applied Finance, Vol.17(2), pp.1450010, 2014.
  22. Almost sure optimal hedging strategy.
    With N. Landon.
    Annals of Applied Probability, Vol. 24(4), pp.1652-1690, 2014.
  23. Weak approximation of averaged diffusion processes.
    With M. Miri.
    Stochastic Processes and their Applications, Vol.124, pp.475-504, 2014.
    Preprint available on HAL.
  24. Preliminary control variates to improve empirical regression methods.
    With T. Ben Zineb.
    Monte Carlo Methods and Applications, Vol.19(4), pp.331-354, 2013.
    Preprint available on HAL.
  25. Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition.
    With C. Geiss and S. Geiss.
    Stochastic Processes and their Applications, Vol.122(5), pp.2078-2216, 2012.
    Preprint available on HAL.
  26. Stochastic expansion for the pricing of call options with discrete dividends.
    With P. Etore.
    Applied Mathematical Finance, Vol.19(3), pp.233-264, 2012.
    Preprint available on HAL and ssrn.
  27. Analytical formulas for local volatility model with stochastic rates.
    With E. Benhamou and M. Miri.
    Quantitative Finance, Vol.12(2), pp.185-198, 2012.
    Preprint available on HAL and ssrn.
  28. The tracking error rate of the Delta-Gamma hedging strategy.
    With A. Makhlouf.
    Mathematical Finance, Vol. 22(2), pp.277-309, 2012.
    Preprint available on HAL and ssrn.
  29. Solving BSDE with adaptive control variate.
    With C. Labart.
    SIAM Journal on Numerical Analysis, Vol.48(1), pp.257-277, 2010.
    Preprint available on HAL.
  30. Time dependent Heston model.
    With E. Benhamou and M. Miri.
    SIAM Journal on Financial Mathematics, Vol.1, pp.289-325, 2010.
    Preprint available on HAL and ssrn.
  31. L2-time regularity of BSDEs with irregular terminal functions.
    With A. Makhlouf.
    Stochastic Processes and their Applications, Vol.120, pp.1105-1132, 2010.
    Preprint available on HAL.
  32. Expansion formulas for European options in a local volatility model.
    With E. Benhamou and M. Miri.
    International Journal of Theoretical and Applied Finance, Vol.13(4), pp.602-634, 2010.
    Preprint available on HAL and ssrn.
  33. Stopped diffusion processes: overshoots and boundary correction.
    With S. Menozzi.
    Stochastic Processes and their Applications, Vol.120, pp.130-162, 2010.
    Preprint available on arXiv and HAL.
  34. Smart expansion and fast calibration for jump diffusion.
    With E. Benhamou and M. Miri.
    Finance and Stochastics, Vol.13(4), pp.563-589, 2009.
    Preprint available on arXiv, HAL and ssrn.
  35. Sharp estimates for the convergence of the density of the Euler scheme in small time.
    With C. Labart.
    Electronic Communications in Probability, Vol.13, pp.311-322, 2008. Erratum.
    Preprint available on HAL.
  36. LAMN property for hidden processes: the case of integrated diffusions.
    With A. Gloter.
    Annales de l'IHP (B) Probability and Statistics, Vol.44(1), pp.104-128, 2008.
    Preprint available on arXiv and HAL.
  37. Error expansion for the discretization of Backward Stochastic Differential Equations
    With C. Labart.
    Stochastic Processes and their Applications, Vol.117(7), pp.803-829, 2007.
    Preprint available on arXiv and HAL.
  38. Discrete sampling of functionals of Itô processes.
    With S. Menozzi.
    Séminaire de Probabilités, Vol.XL, pp.355-375, 2007. pdf file
  39. Numerical methods for the pricing of Swing options: a stochastic control approach.
    With C. Barrera-Esteve, F. Bergeret, C. Dossal, A. Meziou, R. Munos and D. Reboul-Salze.
    Methodology and Computing in Applied Probability, Vol.8(4), pp.517-540, 2006.
    Preprint available on HAL.
  40. Boundary sensitivities for diffusion processes in time dependent domains.
    With C. Costantini and N. El Karoui.
    Applied Mathematics and Optimization, Vol.54(2), pp.159-187, 2006. pdf file
  41. Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations.
    With J.P. Lemor and X. Warin.
    Bernoulli, Vol.12(5), pp.889-916, 2006. pdf file
  42. Discretization and simulation of Zakai equation.
    With G. Pagès, H. Pham and J. Printemps.
    SIAM Journal on Numerical Analysis, Vol.44(6), pp.2505-2538, 2006. pdf file
  43. Sequential control variates for functionals of Markov processes.
    With S. Maire.
    SIAM Journal on Numerical Analysis, Vol.43(3), pp.1256-1275, 2005. pdf file
  44. A regression-based Monte-Carlo method to solve backward stochastic differential equations.
    With J.P. Lemor and X. Warin.
    Annals of Applied Probability, Vol.15(3), pp.2172-2002, 2005. pdf file
  45. Sensitivity analysis using Itô-Malliavin calculus and martingales. Application to stochastic optimal control.
    With R. Munos.
    SIAM Journal on Control and Optimization, Vol.43(5), pp.1676-1713, 2005. pdf file
    Sensitivity analysis using Itô-Malliavin calculus and martingales. Numerical implementation. Rapport interne #520 du CMAP.
  46. Symmetrized Euler scheme for an efficient approximation of reflected diffusions.
    With M. Bossy and D. Talay.
    Journal of Applied Probability, Vol.4(3), pp.877-889, 2004. pdf file(308K).
  47. Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme.
    With S. Menozzi.
    Stochastic Processes and their Applications, Vol.112(2), pp.201-223, 2004. pdf file
  48. Nonparametric estimation of scalar diffusions based on low frequency data.
    With M. Hoffmann and M. Reiss.
    Annals of Statistics, Vol.32(5), pp.2223-2253, 2004. pdf file (252K)
  49. Représentation de Feynman-Kac dans des domaines temps-espace et sensibilité par rapport au domaine (Feynman-Kac's representation in time-space domains and sensitivity with respect to the domain).
    With C. Costantini and N. El Karoui.
    Comptes Rendus Mathématiques, Vol.337(5), pp.337-342, 2003.
  50. Computation of Greeks for barrier and lookback options using Malliavin calculus.
    With A. Kohastu-Higa.
    Electronic Communications in Probability, Vol.8, pp.51-62, 2003. pdf file
  51. LAN property for ergodic diffusions with discrete observations.
    Annales de l'IHP (B) Probabilités et statistiques, Vol.38(5), pp.711-737, 2002. pdf file
  52. Euler schemes and half-space approximation for the simulation of diffusion in a domain.
    ESAIM Probability and Statistics, Vol.5, pp.261-297, 2001. pdf file
  53. Local asymptotic mixed normality property for elliptic diffusion: a Malliavin calculus approach.
    Bernoulli, Vol.7(6), pp.899-912, 2001. pdf file
  54. Erratum: A correction note to “Discrete time hedging errors for options with irregular payoffs”. Finance and Stochastics, 2014.
  55. Discrete time hedging errors for options with irregular pay-offs.
    With E. Temam.
    Finance and Stochastics, Vol.5(3), pp.357-367, 2001. pdf file
  56. Weak approximation of killed diffusion using Euler schemes.
    Stochastic Processes and their Applications, Vol.87, pp.167-197, 2000. pdf file
  57. Schéma d'Euler discret pour diffusion multidimensionnelle tuée.
    C.R. Acad. Sci. Paris, Série I, Vol.328, pp.515-520, 1999.
  58. Schéma d'Euler continu pour des diffusions tuées et options barrière.
    C.R. Acad. Sci. Paris, Série I, Vol.326, pp.1411-1414, 1998.

CHAPTERS/BOOKS

  1. Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear.
    Monte-Carlo methods and stochastic processes: from linear to non-linear 327 pages, CRC Press, August 2016.  You can buy it on Amazon or CRC Press.
  2. Introduction to stochastic calculus and to the resolution of PDEs using Monte Carlo simulations.
    Springer SEMA/SIMAI series, Proceedings of the XV Spanish-French School, Malaga, september 2012.
    Edited by F. Coquel, C. Pares, C. Vasques Cendon, 2013.
  3. Méthodes de Monte-Carlo et processus stochastiques: du linéaire au non-linéaire.
    Méthodes de Monte-Carlo et processus stochastiques: du linéaire au non-linéaire 252 pages, Editions de l’Ecole Polytechnique, 2013. You can buy it on Amazon or GibertJoseph.
  4. Asymptotic and non asymptotic approximations for option valuation.
    With R. Bompis.
    In Recent Developments in Computational Finance:Foundations, Algorithms and Applications, Thomas Gerstner and Peter Kloeden (Ed.), World Scientific Publishing Company. Available on HAL and ssrn, 2012.
  5. New Approximations in Local Volatility Models.
    With A. Suleiman.
    Forthcoming in Y. Kabanov, M. Rutkowski, T. Zariphopoulou, editors, Inspired by Finance. The Musiela Festschrift. Springer, 2014.
    Preprint available on HAL and ssrn, 2012.
  6. Les outils stochastiques des marchés financiers : une visite guidée de Einstein à Black-Scholes.
    With N. El Karoui.
    Les outils stochastiques des marchés financiers 221 pages, Editions de l’Ecole Polytechnique, 2011.
    You can download a simplified version without figures and exercises here. Or you can buy the full version on Amazon or Ellipses.
  7. Fractional smoothness and applications in Finance.
    With S. Geiss.
    In G. Di Nunno and B. Oksendal, editors, AMaMeF. Springer Verlag, 2011.
    Available on HAL.
  8. Advanced Monte Carlo methods for barrier and related exotic options.
    Handbook of Numerical Analysis, Vol.XV. Elsevier.
    Special Volume: Mathematical Modeling and Numerical Methods in Finance.
    Editor: P.G. Ciarlet. Guest Editors: Alain Bensoussan and Qiang Zhang, pp.497-528, 2009.
    Preprint available on HAL and ssrn.

PROCEEDINGS

  1. Asymptotic equivalence between boundary perturbations and discrete exit times: application to simulation schemes.
    In L. Plaskota and H. Wozniakowski, editors, Proceedings of the 9th International Conference on Monte Carlo and Quasi- Monte Carlo Methods in Scientific Computing (MCQMC’2010), 15-20 August 2010. Springer, 2011.
  2. A sequential Monte Carlo algorithm for solving BSDEs.
    With C. Labart.
    Proceedings of "6th International Congress on Industrial and Applied Mathematics", ICIAM 2007 at ETH Zurich, Suisse. Wiley Inter Science. PAMM, 7(1), pp.1081801-1081802, Dec 2007.
  3. A class of financial products and models where super-replication prices are explicit.
    With L. Carassus and E. Temam. 
    Proceedings of the "Ritsumeikan International Symposium on Stochastic Processes and Applications to Mathematical Finance" at Ritsumeikan University, Kusatsu, Japan, March 2006. Edited by J. Akahori, S. Ogawa, S. Watanabe. World Scientific, pp.67-84, 2007. pdf file
  4. Numerical simulation of BSDEs using empirical regression methods: theory and practice.
    With J.P. Lemor.
    Proceedings of the "Fifth Colloquium on BSDEs" (29th May - 1st June 2005, Shangai).
    Available on ArXiv and HAL.
  5. Sequential Monte Carlo domain decomposition for the Poisson equation.
    With S. Maire.
    Proceedings of the 17th IMACS World Congress, Scientific Computation, Applied Mathematics and Simulation (11-15 July 2005, Paris).
  6. A spectral Monte Carlo method for the Poisson equation.
    With S. Maire.
    Proceedings of the "IVth IMACS Seminar on Monte Carlo Methods MCM-2003" (15-19 September 2003, Berlin). Monte Carlo Methods and Applications, Vol.10(3-4), pp.275-285, 2004.
  7. Revisiting the Greeks for European and American options.
    Proceedings of the "International Symposium on Stochastic Processes and Mathematical Finance" at Ritsumeikan University, Kusatsu, Japan, March 2003. Edited by J. Akahori, S. Ogawa, S. Watanabe. World Scientific, pp.53-71, 2004. pdf file
  8. Monte Carlo evaluation of Greeks for multidimensional barrier and lookback options.
    With G. Bernis and A. Kohastu-Higa.
    Proceedings of the "Workshop on the Application of Malliavin calculus in finance", Rocquencourt (France), December 13-14, 2001. Mathematical Finance, Vol.13(1), pp.99-113, 2003. pdf file
  9. Efficient schemes for the weak approximation of reflected diffusions.
    Proceedings of the "International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations", Monaco, July 3-5, 2000. Monte Carlo Methods and Applications, Vol.7(1-2), pp.193-202, 2001. pdf file

PREPRINTS

  • Analysis of the zigzag convergence for barrier options with binomial trees.
    Prépublication # 536 du laboratoire PMA, 24 pages, 1999. Unpuplished manuscript.
  • Arbitrage free cointegrated models in gas and oil future markets.
    With G. Benmenzer and C. Jérusalem.
    Preprint available on arXiv and HAL, 2007. Unpuplished manuscript.
  • Solving BSDE with adaptive control variate. A note on the rate of convergence of the operator $Pk$.
    With C. Labart.
    Technical note available on HAL, 2009. Unpuplished manuscript.
  • A new sequential algorithm for L2-approximation and application to Monte-Carlo integration.
    With K. Surana.
    Preprint available on HAL, 2014.
  • Convergence rate of strong approximations  of compound random maps.
    With M. Mrad.
    Preprint available on HAL, 2015.
  • Rare event simulation related to financial risks: efficient estimation and sensitivity analysis.With A. Agarwal, S. De Marco and G. Liu.
    Preprint available on hal-01219616, 2015.
  • Model-adaptive optimal discretization of stochastic integrals. E. Gobet and U. Stazhynski, 2017.
  • Analytical approximations of non-linear SDEs of McKean-Vlasov type. E. Gobet and S. Pagliarani, 2017.
  • Finite variance unbiased estimation of stochastic differentiel equations. A. Agarwal and E. Gobet, 2017.

OTHER PUBLICATIONS

  • Evènements rares: comment calculer l'imprévisible?
    Cahiers de l'Institut Louis Bachelier, Vol.17, avril 2015.
  • Comment définir des dates d'intervention optimales sur les marchés peu liquides?
    Cahiers de l'Institut Louis Bachelier, Vol.11, octobre 2013.
  • Formules rapides de valorisation d'options et calibration temps-réel.
    With E. Benhamou and M. Miri.
    Cahiers de l'Institut Louis Bachelier, Vol.2, juillet 2011.
  • Mathématiques et Finance.
    With G. Pagès and M. Yor.
    "La Lettre de l'Académie des sciences", numéro 13, 11 pages, Automne 2004. ps file
  • Les mathématiques appliquées au coeur de la finance.
    "Images des mathématiques 2004" (édité par le CNRS) pp.58-63, 2004. ps file
  • HDR: Contributions à la simulation et à l'analyse de discrétisation de processus, et applications.
    November 24, 2003. pdf file

PhD STUDENTS

  1. Stéphane Menozzi (2001-2004): currently Professor at Evry University.
  2. Jean-Philippe Lemor (2002-2005): currently Senior Quant at BNP Paribas.
  3. Céline Labart (2004-2007): currently assistant professor at Université de Savoie.
  4. Azmi Makhlouf (2006-2009): currently assistant professor at ENIT, Tunisie.
  5. Mohammed Miri (2006-2009): currently Head of Research at Thomson Reuters.
  6. Tarik Ben Zineb (2009-2012): currently Quant at Thomson Reuters
  7. Nicolas Landon (2009-2012): currently Senior Quant at Deutsche Bank
  8. Romain Bompis (2010-2013): currently Quant at Credit Agricole - GRO.
  9. Gang Liu (2013-2016): currently Quant à Square Point.
  10. Gustaw Matulevicz (2014-2017)
  11. Isaque Pimentel (2015- )
  12. Uladzislau Stazhynki (2016 - )
  13. Margaux Faucher (2016 - )
  14. Florian Bourgey (2017-  )
  15. Maxime Grangereau (2017 - )
   

CO-AUTHORS



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