On the Multi-Dimensional Controller and Stopper Games

Details On the Multi-Dimensional Controller and Stopper Games On the Multi-Dimensional Controller and Stopper Games

2010-09-05

arxiv.org/abs/1009.0932v6

Mathematics

Optimization and Control

Key words: Controller-stopper games, weak dynamic programming principle, viscosity solutions, robust optimal stopping. 29 page

Scientific paper

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.

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