OPTIMAL SWITCHING OF ONE-DIMENSIONAL REFLECTED BSDES AND ASSOCIATED MULTIDIMENSIONAL BSDES WITH OBLIQUE REFLECTION

In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs) where the generators, the terminal values, and the barriers are all switched with positive costs. The value process is characterized by a system of multidimensional RBSDEs with oblique reflection, whose existence and uniqueness are by no means trivial and are therefore carefully examined. Existence is shown using both methods of the Picard iteration and penalization, but under some different conditions. Uniqueness is proved by representation either as the value process to our optimal switching problem for one-dimensional RBSDEs or as the equilibrium value process to a stochastic differential game of switching and stopping. Finally, the switched RBSDE is interpreted as a real option.