On the Multi-Dimensional Controller and Stopper Games

2010/09/05 by Bayraktar, Erhan, Huang, Yu-Jui · 3 citations
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paper · doi:10.48550/arxiv.1009.0932

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.

Cited by

• Feedback stopping rules in path-dependent controller-stopper games
• A Nonlinear Snell Envelope Representation for Path-Dependent Controller-Stopper Games
• Global regularity of the value function in a stopper vs. singular-controller game

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