The Annals of Probability
- Ann. Probab.
- Volume 36, Number 4 (2008), 1495-1527.
Martingale approach to stochastic differential games of control and stopping
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.
Ann. Probab., Volume 36, Number 4 (2008), 1495-1527.
First available in Project Euclid: 29 July 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 93E20: Optimal stochastic control 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91A15: Stochastic games
Secondary: 91A25: Dynamic games 60G44: Martingales with continuous parameter
Karatzas, Ioannis; Zamfirescu, Ingrid-Mona. Martingale approach to stochastic differential games of control and stopping. Ann. Probab. 36 (2008), no. 4, 1495--1527. doi:10.1214/07-AOP367. https://projecteuclid.org/euclid.aop/1217360977