Session S17 - Stochastic Systems: Analysis, Numerics and Applications

Tuesday, July 13, 13:00 ~ 13:35 UTC-3

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

Yuri Saporito

School of Applied Mathematics, Getulio Vargas Foundation, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we present a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [QF, 2019, originally published in 2009], where the functional Itô calculus was developed to deal with path-dependent financial derivatives contracts. More specifically, we generalize the Deep Galerkin 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 from the Financial Mathematics literature that show the capabilities of the method under very different situations.

Joint work with Zhaoyu Zhang (University of Southern California).

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