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In this paper, we prove new convergence results improving the ones byChassagneux, Elie and Kharroubi [Ann. Appl. Probab. 22 (2012) 971--1007] forthe discrete-time approximation of multidimensional obliquely reflected BSDEs.These BSDEs, arising in the study of switching problems, were considered by Huand Tang [Probab. Theory Related Fields 147 (2010) 89--121] and generalized byHamad\`ene and Zhang [Stochastic Process. Appl. 120 (2010) 403--426] andChassagneux, Elie and Kharroubi [Electron. Commun. Probab. 16 (2011) 120--128].Our main result is a rate of convergence obtained in the Lipschitz setting andunder the same structural conditions on the generator as the one required forthe existence and uniqueness of a solution to the obliquely reflected BSDE.

Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems