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

Abstract

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.

arXiv admin note: substantial text overlap with arXiv:2006.01496

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• A regression-based Monte Carlo method to solve backward stochastic differential equations
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Cited by in corpus (3)

• Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality
• Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance
• Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations