Work

Convergence of particles and tree based scheme for singular FBSDEs

Year: 2025

Type: article

Abstract: We study an implementation of the theoretical splitting scheme introduced in Chassagneux and Yang (J. Comput. Phys. 468 (2022) 111459) for singular FBSDEs (Carmona and Delarue, Probab. Theory Relat. Fields 157 (2013) 333–388) and their associated quasi-linear degenerate PDEs. The fully implementable algorithm is based on particles approximation of the transport operator and tree like approximation of the diffusion operator appearing in the theoretical splitting. We prove the convergence with a rate of our numerical method under some reasonable conditions on the coefficients functions. This validates a posteriori some numerical results obtained in Chassagneux and Yang (J. Comput. Phys. 468 (2022) 111459). We conclude the paper with a numerical section presenting various implementations of the algorithm and discussing their efficiency in practice.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024086

Authors: Jean-François Chassagneux, Mohan Yang

Institutions: Centre de Recherche en Économie et Statistique, Institut Polytechnique de Paris, ENSAE Paris, Université Paris Cité, Laboratoire de Probabilités, Statistique et Modélisation

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid:

OpenAlex ID: W4407402289