Reflected backward stochastic differential equations in an orthant

Abstract

We consider RBSDE in an orthant with oblique reflection and with time and space dependent coefficients, viz. Z(t)=ε+∫_t^Tb(s, Z(s))ds+∫_t^TR(s, Z(s))dY(s)-∫_t^T‹U(s), dB(s)›with Zi(·)≥0, Yi(·) nondecreasing and Yi(·) increasing only when Zi(·) =0, 1 ≤i ≤d. Existence of a unique solution is established under Lipschitz continuity of b, R and a uniform spectral radius condition onR. On the way we also prove a result concerning the variational distance between the 'pushing parts' of solutions of auxiliary one-dimensional problem.