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

arXiv: https://arxiv.org/abs/1911.12231 · HTML: https://mlsanity.com/paper/1911.12231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2019.

## Built on by (most cited first, 2 of 2)

- [Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation](https://mlsanity.com/paper/2304.13224/) (2023)
- [KANHedge: Efficient Hedging of High-Dimensional Options Using Kolmogorov-Arnold Network-Based BSDE Solver](https://mlsanity.com/paper/2601.11097/) (2026)

## Abstract (arXiv)

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.