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@inproceedings{rainforth2017opportunities,
  title={On nesting {M}onte {C}arlo estimators},
  author={Rainforth, Tom and Cornish, Robert and Yang, Hongseok and Warrington, Andrew and Wood, Frank},
  booktitle={Proceedings of the 35th International Conference on Machine Learning}, 
  pages={4267--4276}, 
  volume={80}, 
  series={Proceedings of Machine Learning Research}, 
  year={2018}
}
@article{henry2016branching,
  title={Branching diffusion representation of semilinear {PDE}s and {M}onte {C}arlo approximation},
  author={Henry-Labord\`ere, Pierre and Oudjane, Nadia and Tan, Xiaolu and Touzi, Nizar and Warin, Xavier},
  journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume={55},
  number={1},
  pages={184--210},
  year={2019}
}
@article{warin2017variations,
  title={Variations on branching methods for non linear PDEs},
  author={Warin, Xavier},
  journal={arXiv preprint arXiv:1701.07660},
  year={2017}
}
@article{han2017overcoming,
  title={Solving high-dimensional partial differential equations using deep learning},
  author={Han, Jiequn and Jentzen, Arnulf and Weinan, E},
  journal={Proceedings of the National Academy of Sciences},
  volume={115},
  number={34},
  pages={8505--8510},
  year={2018}
}
@article{weinan2017deep,
  title={Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations},
  author={E, Weinan and Han, Jiequn and Jentzen, Arnulf},
  journal={Communications in Mathematics and Statistics},
  volume={5},
  number={4},
  pages={349--380},
  year={2017},
  publisher={Springer}
}



@article{beck2017machine,
  title={Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations},
  author={Beck, Christian and E, Weinan and Jentzen, Arnulf},
  journal={Journal of Nonlinear Science},
  volume={29},
  number={4},
  pages={1563--1619},
  year={2019}
}

@article{talay1990expansion,
  title={Expansion of the global error for numerical schemes solving stochastic differential equations},
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}
@article{bergman1995option,
  title={Option pricing with differential interest rates},
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  journal={The Review of Financial Studies},
  volume={8},
  number={2},
  pages={475--500},
  year={1995},
  publisher={Oxford University Press}
}

@article{doumbia2017unbiased,
  title={Unbiased {M}onte {C}arlo estimate of stochastic differential equations expectations},
  author={Doumbia, Mahamadou and Oudjane, Nadia and Warin, Xavier},
  journal={ESAIM: Probability and Statistics},
  volume={21},
  pages={56--87},
  year={2017},
  publisher={EDP Sciences}
}

@article{fournie1999applications,
  title={Applications of {M}alliavin calculus to {M}onte {C}arlo methods in finance},
  author={Fourni{\'e}, Eric and Lasry, Jean-Michel and Lebuchoux, J{\'e}r{\^o}me and Lions, Pierre-Louis and Touzi, Nizar},
  journal={Finance and Stochastics},
  volume={3},
  number={4},
  pages={391--412},
  year={1999},
  publisher={Springer}
}

@book{touzi2012optimal,
  title={Optimal stochastic control, stochastic target problems, and backward {SDE}},
  author={Touzi, Nizar},
  volume={29},
  series={Fields Institute Monographs},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@article{chassagneux2016numerical,
  title={Numerical simulation of quadratic {BSDE}s},
  author={Chassagneux, Jean-Fran{\c{c}}ois and Richou, Adrien and others},
  journal={The Annals of Applied Probability},
  volume={26},
  number={1},
  pages={262--304},
  year={2016},
  publisher={Institute of Mathematical Statistics}
}

@article{chassagneux2014linear,
  title={Linear multistep schemes for {BSDE}s},
  author={Chassagneux, Jean-Fran{\c{c}}ois},
  journal={SIAM Journal on Numerical Analysis},
  volume={52},
  number={6},
  pages={2815--2836},
  year={2014},
  publisher={SIAM}
}

@article{pardoux1990adapted,
  title={Adapted solution of a backward stochastic differential equation},
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  number={1},
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}

@article{gobet2005regression,
  title={A regression-based Monte Carlo method to solve backward stochastic differential equations},
  author={Gobet, Emmanuel and Lemor, Jean-Philippe and Warin, Xavier and others},
  journal={The Annals of Applied Probability},
  volume={15},
  number={3},
  pages={2172--2202},
  year={2005},
  publisher={Institute of Mathematical Statistics}
}

@article{lemor2006rate,
  title={Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations},
  author={Lemor, Jean-Philippe and Gobet, Emmanuel and Warin, Xavier and others},
  journal={Bernoulli},
  volume={12},
  number={5},
  pages={889--916},
  year={2006},
  publisher={Bernoulli Society for Mathematical Statistics and Probability}
}
@article{fahim2011probabilistic,
  title={A probabilistic numerical method for fully nonlinear parabolic {PDE}s},
  author={Fahim, Arash and Touzi, Nizar and Warin, Xavier},
  journal={The Annals of Applied Probability},
  pages={1322--1364},
  year={2011},
  publisher={JSTOR}
}

@article{bouchard2017numerical,
  title={Numerical approximation of {BSDE}s using local polynomial drivers and branching processes},
  author={Bouchard, Bruno and Tan, Xiaolu and Warin, Xavier and Zou, Yiyi},
  journal={Monte Carlo Methods and Applications},
  volume={23},
  number={4},
  pages={241--263},
  year={2017},
  publisher={De Gruyter}
}
@article{bouchard2017numerical2,
  title={Numerical approximation of general Lipschitz {BSDE}s with branching processes},
  author={Bouchard, Bruno and Tan, Xiaolu and Warin, Xavier},
  journal={ESAIM: Proceedings and Surveys},
  volume={65},
  pages={309--329},
  year={2019}
}

@misc{bauke2011tina,
  title={Tina’s random number generator library},
  author={Bauke, Heiko},
  year={2011},
  publisher={August}
}

@article{kahl2006fast,
  title={Fast strong approximation Monte Carlo schemes for stochastic volatility models},
  author={Kahl, Christian and J{\"a}ckel, Peter},
  journal={Quantitative Finance},
  volume={6},
  number={6},
  pages={513--536},
  year={2006},
  publisher={Taylor \& Francis}
}
@article{warin2018nesting,
  title={Nesting {M}onte {C}arlo for high-dimensional non linear {PDE}s},
  author={Warin, Xavier},
  journal={Monte Carlo Methods and Applications},
  volume={24},
  number={4},
  pages={225--247},
  year={2018}
}

@article{bouchard2004discrete,
  title={Discrete-time approximation and {M}onte-{C}arlo simulation of backward stochastic differential equations},
  author={Bouchard, Bruno and Touzi, Nizar},
  journal={Stochastic Processes and their applications},
  volume={111},
  number={2},
  pages={175--206},
  year={2004},
  publisher={Elsevier}
}
@article{cheridito2007second,
  title={Second-order backward stochastic differential equations and fully nonlinear parabolic {PDE}s},
  author={Cheridito, Patrick and Soner, H Mete and Touzi, Nizar and Victoir, Nicolas},
  journal={Communications on Pure and Applied Mathematics},
  volume={60},
  number={7},
  pages={1081--1110},
  year={2007},
  publisher={Wiley Online Library}
}
@article{tan2013splitting,
  title={A splitting method for fully nonlinear degenerate parabolic PDEs},
  author={Tan, Xiaolu},
  journal={Electronic Journal of Probability},
  volume={18},
  year={2013},
  publisher={The Institute of Mathematical Statistics and the Bernoulli Society}
}

@article{heston1993closed,
  title={A closed-form solution for options with stochastic volatility with applications to bond and currency options},
  author={Heston, Steven L},
  journal={The Review of Financial Studies},
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  number={2},
  pages={327--343},
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}

@article{weinan2017linear,
  title={Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations},
  author={E, Weinan and Hutzenthaler, Martin and Jentzen, Arnulf and Kruse, Thomas},
  journal={SAM Research Report},
  volume={2017},
  year={2017},
  publisher={ETH Zurich}
}

@article{weinan2016multilevel,
  title={On multilevel {P}icard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations},
  author={E, Weinan and Hutzenthaler, Martin and Jentzen, Arnulf and Kruse, Thomas},
  journal={Journal of Scientific Computing},
  volume={79},
  number={3},
  pages={1534--1571},
  year={2019}
}

@article{hutzenthaler2017multi,
  title={Multi-level {P}icard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities},
  author={Hutzenthaler, Martin and Kruse, Thomas},
  journal={SIAM Journal on Numerical Analysis},
  volume={58},
  number={2},
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  year={2020}
}

@book{fleming2006controlled,
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  publisher={Springer Science \& Business Media}
}

@article{ishii1990viscosity,
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}

@book{quarteroni2000methodes,
  title={M{\'e}thodes num{\'e}riques pour le calcul scientifique: programmes en {MATLAB}},
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  publisher={Springer Science \& Business Media}
}

@article{azaiez1993methodes,
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}

@article{feinerman1974polynomial,
  title={Polynomial approximation},
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}


@book{soardi1984serie,
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}
@inproceedings{smolyak1963quadrature,
  title={Quadrature and interpolation formulas for tensor products of certain classes of functions},
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}

@article{bungartz2004sparse,
  title={Sparse grids},
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  year={2004},
  publisher={Cambridge University Press}
}

@phdthesis{pfluger2010spatially,
  title={Spatially adaptive sparse grids for high-dimensional problems},
  author={Pfl{\"u}ger, Dirk Michael},
  year={2010},
  school={Technische Universit{\"a}t M{\"u}nchen}
}

@book{bungartz1992dunne,
  title={D{\"u}nne Gitter und deren Anwendung bei der adaptiven L{\"o}sung der dreidimensionalen Poisson-Gleichung},
  author={Bungartz, Hans-Joachim},
  year={1992},
  publisher={Technische Universit{\"a}t M{\"u}nchen}
}

@article{gerstner2003dimension,
  title={Dimension--adaptive tensor--product quadrature},
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  journal={Computing},
  volume={71},
  number={1},
  pages={65--87},
  year={2003},
  publisher={Springer}
}

@article{ma2009adaptive,
  title={An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations},
  author={Ma, Xiang and Zabaras, Nicholas},
  journal={Journal of Computational Physics},
  volume={228},
  number={8},
  pages={3084--3113},
  year={2009},
  publisher={Elsevier}
}

@phdthesis{reisinger2004numerische,
  title={Numerische Methoden f{\"u}r hochdimensionale parabolische Gleichungen am Beispiel von Optionspreisaufgaben},
  author={Reisinger, Christoph},
  year={2004}
}

@article{leentvaar2008coordinate,
  title={On coordinate transformation and grid stretching for sparse grid pricing of basket options},
  author={Leentvaar, CCW and Oosterlee, CW},
  journal={Journal of Computational and Applied Mathematics},
  volume={222},
  number={1},
  pages={193--209},
  year={2008},
  publisher={Elsevier}
}

@article{bokanowski2013adaptive,
  title={An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations},
  author={Bokanowski, Olivier and Garcke, Jochen and Griebel, Michael and Klompmaker, Irene},
  journal={Journal of Scientific Computing},
  volume={55},
  number={3},
  pages={575--605},
  year={2013},
  publisher={Springer}
}

@incollection{bouchard2012monte,
  title={Monte-{C}arlo valuation of American options: facts and new algorithms to improve existing methods},
  author={Bouchard, Bruno and Warin, Xavier},
  booktitle={Numerical methods in finance},
  pages={215--255},
  year={2012},
  publisher={Springer}
}

@inproceedings{bungartz1996concepts,
  title={Concepts for higher order finite elements on sparse grids},
  author={Bungartz, Hans-Joachim},
  booktitle={Houston Journal of Mathematics: Proceedings of the 3rd Int. Conf. on Spectral and High Order Methods, Houston},
  pages={159--170},
  year={1996}
}

@article{bungartz1997multigrid,
  title={A multigrid algorithm for higher order finite elements on sparse grids},
  author={Bungartz, Hans-Joachim},
  journal={Electronic Transactions on Numerical Analysis},
  volume={6},
  pages={63--77},
  year={1997},
  publisher={Kent State University}
}

@inproceedings{makassikis2008large,
  title={Large scale distribution of stochastic control algorithms for gas storage valuation},
  author={Makassikis, Constantinos and Vialle, St{\'e}phane and Warin, Xavier},
  booktitle={Parallel and Distributed Processing, 2008. IPDPS 2008. IEEE International Symposium on},
  pages={1--8},
  year={2008},
  organization={IEEE}
}

@inproceedings{vialle2008stochastic,
  title={Stochastic control optimization \& simulation applied to energy management: From 1-D to ND problem distributions, on clusters, supercomputers and Grids},
  author={Vialle, St{\'e}phane and Warin, Xavier and Makassikis, Constantinos and Mercier, Patrick},
  booktitle={Grid@ Mons conference},
  year={2008}
}

@incollection{warin2012gas,
  title={Gas storage hedging},
  author={Warin, Xavier},
  booktitle={Numerical Methods in Finance},
  pages={421--445},
  year={2012},
  publisher={Springer}
}

@article{camilli1995approximation,
  title={An approximation scheme for the optimal control of diffusion processes},
  author={Camilli, Fabio and Falcone, Maurizio},
  journal={ESAIM: Mathematical Modelling and Numerical Analysis},
  volume={29},
  number={1},
  pages={97--122},
  year={1995},
  publisher={EDP Sciences}
}

@article{munos2005consistency,
  title={Consistency of a simple multidimensional scheme for Hamilton--Jacobi--Bellman equations},
  author={Munos, R{\'e}mi and Zidani, Hasnaa},
  journal={Comptes Rendus Mathematique},
  volume={340},
  number={7},
  pages={499--502},
  year={2005},
  publisher={Elsevier}
}

@article{warin2016some,
  title={Some non-monotone schemes for time dependent Hamilton--Jacobi--Bellman equations in stochastic control},
  author={Warin, Xavier},
  journal={Journal of Scientific Computing},
  volume={66},
  number={3},
  pages={1122--1147},
  year={2016},
  publisher={Springer}
}

@article{warin2014adaptive,
  title={Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic control},
  author={Warin, Xavier},
  journal={arXiv preprint arXiv:1408.4267},
  year={2014}
}
@article{pereira1991multi,
  title={Multi-stage stochastic optimization applied to energy planning},
  author={Pereira, Mario VF and Pinto, Leontina MVG},
  journal={Mathematical programming},
  volume={52},
  number={1-3},
  pages={359--375},
  year={1991},
  publisher={Springer}
}

@article{benders2005partitioning,
  title={Partitioning procedures for solving mixed-variables programming problems},
  author={Benders, JF},
  journal={Computational Management Science},
  volume={2},
  number={1},
  pages={3--19},
  year={2005},
  publisher={Springer}
}

@article{pereira1999application,
  title={Application of stochastic dual DP and extensions to hydrothermal scheduling},
  author={Pereira, Mario and Campodonico, Nora and Kelman, Rafael},
  journal={Online Rep., http://www. psr-inc. com. br/reports. asp, PSRI Technical Rep},
  volume={12},
  pages={99},
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