PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations

2020/03/04 by Yuri F. Saporito, Zhaoyu Zhang, Saporito, Yuri F. +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Finance (q-fin.CP) #Energy Load and Power Forecasting #FOS: Computer and information sciences #FOS: Economics and business #Fractional Differential Equations Solutions #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2003.02035

openalex publication_date 2020/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional Itô calculus was developed to deal with path-dependent financial derivatives contracts. More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with these equations. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.

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