A deep solver for BSDEs with jumps

Alessandro Gnoatto, Athena Picarelli, Marco Patacca

Publication date: 8 November 2022

Abstract: The aim of this work is to propose an extension of the Deep BSDE solver by Han, E, Jentzen (2017) to the case of FBSDEs with jumps. As in the aforementioned solver, starting from a discretized version of the BSDE and parametrizing the (high dimensional) control processes by means of a family of ANNs, the BSDE is viewed as model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity by introducing, in the latter case, an approximation with finitely many jumps of the forward process.

Has companion code repository: https://github.com/alessandrognoatto/deepbsdesolverwithjumps

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

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