Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM

Abstract

Building heavily on the recent nice paper [Weinan E-al (2017)], we introduce a primal-dual method for solving BSDEs based on the use of neural networks, stochastic gradient descent and a dual formulation of stochastic control problems. Our algorithm is illustrated with two examples relevant in Mathematical Finance: the pricing of counterparty risk and the computation of initial margin.