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Exploring backward stochastic differential equations and deep learning for high-dimensional partial differential equations and European option pricing

Many phenomena in our world can be described as differential equations in high dimensions. However, they are notoriously challenging to solve numerically due to the exponential growth in computational cost with increasing dimensions. This thesis explores an algorithm, known as deep BSDE, for solving high-dimensional partial differential equations and applies it to finance, namely European option pricing. In addition, an implementation of the method is provided that seemingly shortens the runtime by a factor of two, compared with the results in previous studies. From the results, we can conclude that the deep BSDE method does handle high-dimensional problems well. Lastly, the thesis gives the relevant prerequisites required to be able to digest the theory from an undergraduate level.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-62879
Date January 2023
CreatorsLeung, Jonathan
PublisherMälardalens universitet, Akademin för utbildning, kultur och kommunikation
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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