On the Multi-Dimensional Controller-and-Stopper Games

SIAM Journal on Control and Optimization (2013), Vol. 51, No. 2, pp. 1263-1297.

35 Pages Posted: 1 Feb 2014

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Date Written: January 6, 2013

Abstract

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.

Keywords: controller-stopper games, weak dynamic programming principle, viscosity solutions, robust optimal stopping

JEL Classification: C72, C73

Suggested Citation

Bayraktar, Erhan and Huang, Yu-Jui, On the Multi-Dimensional Controller-and-Stopper Games (January 6, 2013). SIAM Journal on Control and Optimization (2013), Vol. 51, No. 2, pp. 1263-1297., Available at SSRN: https://ssrn.com/abstract=2388192

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yu-Jui Huang (Contact Author)

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
23
Abstract Views
425
PlumX Metrics