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

to appear in Machine Learning And Data Sciences For Financial Markets: A Guide To Contemporary Practices. Ed. by A. Capponi. and C.A. Lehalle. Cambridge University Press, 2021. Chap. New Frontiers for Stochastic Control in FinanceInternational audienceThis 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