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Neural networks-based algorithms for stochastic control and PDEs in finance

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arxiv 2101.08068 v2 pith:KA3DKONJ submitted 2021-01-20 math.OC q-fin.CP

Maximilien Germain , Huyên Pham , Xavier Warin This is my paper · ORCID
classification math.OCq-fin.CP
keywords algorithmsfinancialnonlinearapplicationsarisingcasecompareconclude
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This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and derivative pricing in financial engineering. We survey recent results in the literature, present new developments, notably in the fully nonlinear case, and compare the different schemes illustrated by numerical tests on various financial applications. We conclude by highlighting some future research directions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neural feedback approximation for stochastic control with degenerate diffusions: error estimates and numerical analysis

    math.OC 2026-07 conditional novelty 6.0 of 10

    Direct neural feedback learning for time-discrete stochastic control admits an averaged value-error bound without transition-density assumptions, covering degenerate and deterministic dynamics.

  2. PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning

    math.OC 2025-05 conditional novelty 6.0 of 10

    PADAM runs K differently averaged Adam trajectories in parallel, selects the one with the smallest test error, and achieves the best optimization error in nearly all of 13 tested scientific machine learning problems w...

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