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

Maximilien Germain, Huyen PHAM, Xavier Warin

Abstract: This paper presents machine learning techniques and deep reinforcement learning- based algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and derivative pric- ing 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 high- lighting some future research directions.