An existence theorem for multidimensional BSDEs with mixed reflections

Abstract

In this note, we consider the pricing problem for a type of real option, which gives the right to switch investment modes and abandon the investment project before its maturity. The value of this option can be characterized by solutions to multidimensional backward stochastic differential equations (BSDEs) with both normal and oblique reflections, whose coefficients are of linear growth and are left-Lipschitz with respect to (w.r.t) y and Lipschitz w.r.t. z. We provide an existence theorem of minimal solutions for BSDEs in this framework.