A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation

This paper focuses on zero-sum stochastic differential games in the framework of forward-backward equations a finite time horizon with both players adopting impulse controls. By means BSDE methods, particular that notion from Peng’s backward semigroups, authors prove dynamic programming principle for upper and lower value functions game. The are then shown to be unique viscosity solutions Hamilton-Jacobi-Bellman-Isaacs double-obstacle. As consequence, uniqueness implies coincide game admits value.