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.
Publié le : 2008-07-15
Classification:
Stochastic games,
control,
optimal stopping,
martingales,
Doob–Meyer decompositions,
stochastic maximum principle,
thrifty control strategies,
93E20,
60G40,
91A15,
91A25,
60G44
@article{1217360977,
author = {Karatzas, Ioannis and Zamfirescu, Ingrid-Mona},
title = {Martingale approach to stochastic differential games of control and stopping},
journal = {Ann. Probab.},
volume = {36},
number = {1},
year = {2008},
pages = { 1495-1527},
language = {en},
url = {http://dml.mathdoc.fr/item/1217360977}
}
Karatzas, Ioannis; Zamfirescu, Ingrid-Mona. Martingale approach to stochastic differential games of control and stopping. Ann. Probab., Tome 36 (2008) no. 1, pp. 1495-1527. http://gdmltest.u-ga.fr/item/1217360977/