Introduction to Solving Quant Finance Problems with Time-Stepped FBSDE and Deep Learning

Bernhard Hientzsch

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Abstract: In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final value problems can be turned into control problems, how time-continuous problems can be turned into time-discrete problems, and how the forward and backward stochastic differential equations (SDE) can be time-stepped. We obtain both forward and backward time-stepped time-discrete stochastic control problems (where forward and backward indicate in which direction the Y SDE is time-stepped) that we will solve with optimization approaches using deep neural networks for the controls and stochastic gradient and other deep learning methods for the actual optimization/learning. We close with examples for the forward and backward methods for an European option pricing problem. Several methods and approaches are new.

Date: 2019-11
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ore
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1911.12231

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