Multidimensional BSDEs with Mixed Reflections and Balance Sheet Optimal Switching Problem

In this paper, we study a system of multidimensional coupled reflected backward stochastic differential equations (RBSDEs) with interconnected generators and barriers and mixed reflections, i.e. oblique and normal reflections. This system of equations is arising in the context of optimal switching problem when both sides of the balance sheet are considered. This problem incorporates both the action of switching between investment modes and the action of abandoning the investment project before its maturity once it becomes unprofitable. Pricing such real options (switch option and abandon option) is equivalent to solve the system of coupled RBSDEs considered in the paper, for which we show the existence of a continuous adapted minimal solution via a Picard iteration method.