Mean-field doubly reflected backward stochastic differential equations

Yinggu Chen; Said Hamadène; Tingshu Mu

doi:10.3934/naco.2022012

Article Contents

2023, Volume 13, Issue 3&4: 431-460. Doi: 10.3934/naco.2022012

This issue Previous Article On path-dependent multidimensional forward-backward SDEs Next Article Optimal pairs trading of mean-reverting processes over multiple assets

Mean-field doubly reflected backward stochastic differential equations

1.
Department of Mathematics, Shandong University, Jinan, Shandong Province, China
2.
Le Mans University, LMM, Avenue Olivier Messiaen, 72085 Le Mans, Cedex 9, France

This paper is dedicated to Professor Jin Ma on the occasion of his 65-th Birthday.

Received: March 2022

Revised: April 2022

Early access: May 2022

Published: September 2023

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Abstract

We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are $ p $-integrable with $ p = 1 $ or $ p>1 $. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two methods do not cover the same set of assumptions.

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Mathematics Subject Classification: 49N80; 91A16; 91G66.

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