Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes

Author:

Barrasso Adrien1,Russo Francesco2

Affiliation:

1. Université d’Evry Val d’Essonne, Laboratoire de Mathématiques et Modélisation, 23 Bd. de France, F-91037 Évry Cedex, France

2. Université d’Evry Mathématiques appliquées, ENSTA Paris, Institut Polytechnique de Paris, 828, boulevard des Maréchaux, F-91120 Palaiseau, France

Abstract

We are interested in path-dependent semilinear PDEs, where the derivatives are of Gâteaux type in specific directions [Formula: see text] and [Formula: see text], being the kernel functions of a Volterra Gaussian process [Formula: see text]. Under some conditions on [Formula: see text] and the coefficients of the PDE, we prove existence and uniqueness of a decoupled mild solution, a notion introduced in a previous paper by the authors. We also show that the solution of the PDE can be represented through BSDEs where the forward (underlying) process is [Formula: see text].

Publisher

World Scientific Pub Co Pte Ltd

Subject

Modeling and Simulation

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