A deep solver for BSDEs with jumps
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866912386049376256 |
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| author | Andersson, Kristoffer Gnoatto, Alessandro Patacca, Marco Picarelli, Athena |
| author_facet | Andersson, Kristoffer Gnoatto, Alessandro Patacca, Marco Picarelli, Athena |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_04349 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A deep solver for BSDEs with jumps Andersson, Kristoffer Gnoatto, Alessandro Patacca, Marco Picarelli, Athena Probability Numerical Analysis Optimization and Control Computational Finance Pricing of Securities 93E20, 65M75, 68T07, 60H10 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. |
| title | A deep solver for BSDEs with jumps |
| topic | Probability Numerical Analysis Optimization and Control Computational Finance Pricing of Securities 93E20, 65M75, 68T07, 60H10 |
| url | https://arxiv.org/abs/2211.04349 |