A deep solver for BSDEs with jumps

2022/11/08 by Alessandro Gnoatto, Andersson, Kristoffer, Gnoatto, Alessandro +4 · 6 citations
Energy · #60H10 #65M75 #68T07 #93E20 #Computational Finance (q-fin.CP) #Energy Efficiency and Management #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2211.04349

openalex publication_date 2022/11/08 · openalex created_date 2022/11/14 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized version of the FBSDE and parametrizing the (high dimensional) control processes by means of a family of artificial neural networks (ANNs), the FBSDE is viewed as a 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. We successfully apply our algorithm to option pricing problems in low and high dimension and discuss the applicability in the context of counterparty credit risk.

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