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 artificial neural networks (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.

A deep solver for BSDEs with jumps

Alessandro Gnoatto
;
Marco Patacca;Athena Picarelli
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 artificial neural networks (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.
BSDE with jumps, Deep BSDE Solver, Neural Networks
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1077666
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