In this paper  we propose a generalization of the Deep Galerking Method (DGM) of \mbox{%DIFAUXCMD dgm Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of \mbox{%DIFAUXCMD fito_dupire  , where the functional It\^o calculus was developed to deal with path-dependent financial derivatives contracts  ]  . 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.
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 It\^o 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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,
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generalization of the Deep Galerking Method (DGM) of \mbox{%DIFAUXCMD dgm
novel numerical method for
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\mbox{%DIFAUXCMD fito_dupire
Dupire
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2009
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. More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos
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2018
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to deal with these equations