On the Multi-Dimensional Controller and Stopper Games
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Erhan Bayraktar & Virginia Young, 2011.
"Proving regularity of the minimal probability of ruin via a game of stopping and control,"
Finance and Stochastics,
Springer, vol. 15(4), pages 785-818, December.
- Erhan Bayraktar & Virginia R. Young, 2007. "Proving Regularity of the Minimal Probability of Ruin via a Game of Stopping and Control," Papers 0704.2244, arXiv.org, revised Aug 2010.
- Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258. Full references (including those not matched with items on IDEAS)