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This paper considers the problem of two-player zero-sum stochasticdifferential game with both players adopting impulse controls in finite horizonunder rather weak assumptions on the cost functions ($c$ and $\chi$ notdecreasing in time). We use the dynamic programming principle and viscositysolutions approach to show existence and uniqueness of a solution for theHamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation (PDE) ofthe game. We prove that the upper and lower value functions coincide.

Zero-sum stochastic differential game in finite horizon involving impulse controls