Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations

Bruno Bouchard, Dylan Possamaï, Xiaolu Tan, and Chao Zhou

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Abstract

We provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. Unlike the previous related approaches in simpler settings, our results do not only rely on a simple application of Itô’s formula and classical estimates, but use crucially appropriate generalizations of deep estimates for supermartingales obtained by Meyer. As an example of application, we prove that reflected BSDEs are well-posed in a general framework which has not been covered so far in the existing literature.

Résumé

Nous proposons dans cet article une approche unifiée permettant l’obtention d’estimées a priori pour des sur-solutions d’EDSR adaptées à des filtrations générales, en particulier non nécessairement quasi-continues à gauche. Contrairement aux approches antérieures de ce problème dans des cadres plus simples, nos résultats ne sont pas la conséquence directe de la formule d’Itô et d’estimées classiques, mais dépendent de manière cruciale de versions appropriées à notre contexte d’estimées obtenues par Meyer pour des sur-martingales. Nous proposons entre autres une application de nos résultats à l’étude de l’existence et de l’unicité de solutions d’EDSR réfléchies dans un cadre général non-couvert par les résultats précédents dans la littérature.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 1 (2018), 154-172.

Dates
Received: 24 July 2015
Revised: 15 September 2016
Accepted: 26 September 2016
First available in Project Euclid: 19 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1519030823

Digital Object Identifier
doi:10.1214/16-AIHP798

Mathematical Reviews number (MathSciNet)
MR3765884

Zentralblatt MATH identifier
06880049

Subjects
Primary: 60H99: None of the above, but in this section

Keywords
Backward SDE Supersolution Doob–Meyer decomposition Reflected backward SDE

Citation

Bouchard, Bruno; Possamaï, Dylan; Tan, Xiaolu; Zhou, Chao. A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 1, 154--172. doi:10.1214/16-AIHP798. https://projecteuclid.org/euclid.aihp/1519030823


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