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This paper analyses a stochastic differential game of control and stopping inwhich one of the players modifies a diffusion process using impulse controls,an adversary then chooses a stopping time to end the game. The paper firstlyestablishes the regularity and boundedness of the upper and lower valuefunctions from which an appropriate variant of the dynamic programmingprinciple (DPP) is derived. It is then proven that the upper and lower valuefunctions coincide so that the game admits a value and that the value of thegame is a unique viscosity solution to a HJBI equation described by a doubleobstacle quasi-integro-variational inequality.

A Viscosity Approach to Stochastic Differential Games of Control and Stopping Involving Impulsive Control