Switching problem and related system of reflected backward SDEs
type: Item
instance of: scholarly article
title: Switching problem and related system of reflected backward SDEs
zbMATH Open document ID: 1191.60056
author: Said Hamadène
author: Jianfeng Zhang
published in: Stochastic Processes and their Applications
publication date: 2010-04-08T00:00:00Z
review text: This paper studies the well posedness of a general system of Backward SDEs with oblique reflections. The authors proves the existence and uniqueness of solutions. One goal of the paper is to extend the work of \textit{S. Hamadène} and \textit{M. Jeanblanc} [Math. Oper. Res. 32, No.~1, 182--192 (2007; Zbl 1276.91100)] by considering Knightian uncertainty and recursive utility. Next they study a very general multi-dimensional RBSDE of which both the generators and the obstacles are interconnected. They prove the existence of solutions by using the notion of the smallest \(g\)-supermartingales introduced by \textit{S. Peng} [Probab. Theory Relat. Fields 113, No. 4, 473--499 (1999; Zbl 0953.60059)] and \textit{S. Peng} and \textit{M. Xu} [Ann. Inst. H. Poincaré, Probab. Statist. 41, No. 3, 605--630 (2005; Zbl 1071.60049)]. A closely related paper is a recent work by \textit{Y. Hu} and \textit{S. Tang} [Probab. Theory Relat. Fields 147, No.~1--2, 89--121 (2010; Zbl 1188.60029)], but the paper under review seems to be more general.
reviewed by: Nikolaos Halidias
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 91B99
zbMATH DE Number: 5690760
zbMATH Keywords: real options
zbMATH Keywords: starting and stopping problem
zbMATH Keywords: switching problem
zbMATH Keywords: backward SDEs
zbMATH Keywords: reflected BSDEs
zbMATH Keywords: oblique reflection
zbMATH Keywords: Snell envelope
zbMATH Keywords: optimal stopping problem
MaRDI profile type: Publication
full work available at URL: j.spa.2010.01.003
OpenAlex ID: W2119993310
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DOI: 10.1016/J.SPA.2010.01.003
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description: scientific article; zbMATH DE number 5690760