2026-09-18T01:28:25Zhttps://elekpub.bib.uni-wuppertal.de/oai/

oai:elekpub.bib.uni-wuppertal.de:80192002025-08-01T00:00:03ZubwhsoaDoctoralThesis

vls/2603noah-balancer_mdapi1elekpub.bib.uni-wuppertal.devdDeep learning-based schemes for solving high-dimensional nonlinear BSDEs and their uncertainty quantificationDeep learning-based schemes for solving high-dimensional nonlinear backward stochastic differential equations and their uncertainty quantificationKapllani, LorencVerfasserautTeng, LongAkademischer BetreuerdgsBergische Universität WuppertalGrad-verleihende InstitutiondggtextthesisTextHochschulschriftthesisdoctoralThesisgwXA-DEWuppertalFebruary 25, 20252025single unitengelectronic resourceremotetext/htmltext/html1 Online-Ressource (xxiii, 114 Seiten) : Illustrationen, DiagrammeComputerOnline-RessourceBackward stochastic differential equations (BSDEs) are widely used in fields such as finance, economics, and physics due to their connection to partial differential equations via the nonlinear Feynman-Kac formula. In option pricing, the solution pair of a BSDE represents both the price and the hedging strategy. While the BSDE under the Black-Scholes framework is linear and admits a closed-form solution, most practical problems involve nonlinear, high-dimensional BSDEs that require advanced numerical methods. Classical schemes often suffer from the curse of dimensionality, prompting the development of deep learning-based approaches. This thesis presents efficient deep learning schemes for solving high-dimensional nonlinear BSDEs and addresses the uncertainty associated with such models. The first part introduces a novel forward scheme that improves stability and accuracy across time steps, demonstrated through various financial examples. The second part develops a differential deep learning framework, training neural networks on both values and derivatives to enhance gradient estimation—crucial for hedging applications. We demonstrate, both theoretically and numerically, that this approach is more efficient than other contemporary deep learning-based schemes. The third part focuses on uncertainty quantification (UQ), proposing the first UQ model tailored to deep BSDE solvers. This model estimates uncertainty from a single run, offering a practical and computationally efficient tool for reliability assessment. Overall, the thesis advances the robustness, accuracy, and interpretability of deep learning methods for solving high-dimensional nonlinear BSDEs.submitted by Lorenc Kapllani, M. Sc.Bergische Universität Wuppertal, Dissertation, 2025backward stochastic differential equationshigh-dimensional problemsdeep neural networksdifferential deep learningmalliavin calculusuncertainty quantificationheteroscedastic nonlinear regressionnonlinear option pricing and hedgingWuppertal518519005urn:nbn:de:hbz:468-2-591210.25926/BUW/0-87199375877813606441Deep learning-based schemes for solving high-dimensional nonlinear BSDEs and their uncertainty quantificationKapllani, LorencDruck-AusgabeHT031234082https://dx.doi.org/10.25926/BUW/0-871https://nbn-resolving.org/urn:nbn:de:hbz:468-2-5912Open AccessCC BY-NC 4.02025-07-11oaDoctoralThesispublic25072220251006110446.0CT009000407s2w-hsswupubwgerUBW:C:C.01 https://elekpub.bib.uni-wuppertal.de//domainresource/static/graphics/connectors/viewerLogo.gifWuppertal : Bergische Universität Wuppertalcc-by-nc https://ub-wuppertal.digibib.net/search/katalog/record/(DE-605)urn%3Anbn%3Ade%3Ahbz%3A468-2-5912 https://elekpub.bib.uni-wuppertal.de/id/8019200 https://elekpub.bib.uni-wuppertal.de/i3f/v20/8019200/manifest https://elekpub.bib.uni-wuppertal.de/proto_ftsearch/8019200