On the multidimensional controller-and-stopper games. (English) Zbl 1268.49045
Summary: We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multidimensional Euclidean space. In this game, the controller affects both the drift and diffusion terms of the state process, and the diffusion term can be degenerate. 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.
MSC:
49N70 | Differential games and control |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
49L20 | Dynamic programming in optimal control and differential games |
91A15 | Stochastic games, stochastic differential games |
91A23 | Differential games (aspects of game theory) |
60J60 | Diffusion processes |