  We study a two-player zero-sum stochastic differential game with both players
adopting impulse controls, on a finite time horizon. The
Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation of the game
turns out to be a double-obstacle quasi-variational inequality, therefore the
two obstacles are implicitly given. We prove that the upper and lower value
functions coincide, indeed we show, by means of the dynamic programming
principle for the stochastic differential game, that they are the unique
viscosity solution to the HJBI equation, therefore proving that the game admits
a value.
