Switching problem and related system of reflected backward SDEs (Q963029)

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.