Martingale approach to stochastic differential games of control and stopping
Probability
2008-08-28 v1
Abstract
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities.
Keywords
Cite
@article{arxiv.0808.3656,
title = {Martingale approach to stochastic differential games of control and stopping},
author = {Ioannis Karatzas and Ingrid-Mona Zamfirescu},
journal= {arXiv preprint arXiv:0808.3656},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AOP367 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)