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This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18].
“Numerical Simulation of BSDEs with Drivers of Quadratic Growth”
Adrien Richou · 1964
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“Reinforcement Learning”
Richard. Sutton and Andrew. Barto · 1998
Earlier work this paper cites.
“Stochastic Controls Hamiltonian Systems and HJB Equations”
Jiongmin Yong and Xunyu Zhou · 1999
Earlier work this paper cites.
“Hedging derivative securities and incomplete markets: an
Dimitris Bertsimas, Leonid Kogan and Andrew. Lo · 2001
Earlier work this paper cites.
“Finite-time Analysis of the Multiarmed Bandit Problem”
Peter Auer, Nicol“‘o Cesa-Bianchi and Paul Fischer · 2002
Earlier work this paper cites.
“Optimal quantization methods and applications to numerical problems in finance”
Gilles Pag“‘es, Huy“ˆen Pham and Jacques Printems · 2004
Earlier work this paper cites.
“Valuation of energy storage: an optimal switching approach”
Ren“’e Carmona and Mike Ludkovski · 2010
Earlier work this paper cites.
“Etude théorique et numérique des équations différentielles stochastiques rétrogrades”, 2010
Adrien Richou · 2010
Cited alongside, same era.
“An approximate dynamic programming algorithm for monotone value functions”
Daniel. Jiang and Warren. Powell · 2015
Cited alongside, same era.
“Numerical Simulation of Quadratic BSDEs”
Jean-Francois Chassagneux and Adrien Richou · 2016
Cited alongside, same era.
“Deep learning”
Ian Goodfellow, Yoshua Bengio and Aaron Courville · 2016
Cited alongside, same era.
“Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”
Weinan E, Jiequn Han and Arnulf Jentzen · 2017
Cited alongside, same era.
“Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM”
Pierre Henry-Labordere · 2017
C“ˆome Hur“’e, Huy“ˆen Pham, Achref Bachouch and Nicolas Langren“’e · 2018
Closest in time.
“A general Monte Carlo algorithm with monotonicity for stochastic control problems” 2018 IMS Annual Meeting on Probability and Statistics, 2018
Steven Kou, Xianhua Peng and Xingbo Xu · 2018
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“Regression Monte Carlo for Microgrid Management”
Clemence Alasseur, Alessandro Balata, Sahar Aziza, Aditya Maheshwari, Peter Tankov and Xavier Warin · 2019
Closest in time.
“A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems”
Alessandro Balata, C“ˆome Hur“’e, Mathieu Lauri“‘ere, Huy“ˆen Pham and Isaque Pimentel · 2019
Closest in time.
“Simulation methods for stochastic storage problems: a statistical learning perspective”
Michael Ludkovski and Aditya Maheshwari · 2019
Closest in time.
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Cited alongside, same era.
“Continuous optimal control approaches to microgrid energy management”
Benjamin Heymann, J.“’ed“’eric Bonnans, Pierre Martinon, Francisco. Silva, Fernando Lanas and Guillermo Jim“’enez-Est“’evez · 2018
Cited alongside, same era.
“Machine Learning for semi linear PDEs”
Quentin Wai-Nam, Joseph Mikael and Xavier Warin · 2019
Closest in time.