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On the Multi-Dimensional Controller and Stopper Games (1009.0932v8)
Published 5 Sep 2010 in math.OC, cs.SY, math.PR, and q-fin.GN
Abstract: We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-BeLLMan equation.