2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167803We 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.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)Probability93E20, 60G40, 91A15 (Primary) 91A25, 60G44 (Secondary)text