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July 2008 Martingale approach to stochastic differential games of control and stopping
Ioannis Karatzas, Ingrid-Mona Zamfirescu
Ann. Probab. 36(4): 1495-1527 (July 2008). DOI: 10.1214/07-AOP367

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.

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Ioannis Karatzas. Ingrid-Mona Zamfirescu. "Martingale approach to stochastic differential games of control and stopping." Ann. Probab. 36 (4) 1495 - 1527, July 2008. https://doi.org/10.1214/07-AOP367

Information

Published: July 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1142.93040
MathSciNet: MR2435857
Digital Object Identifier: 10.1214/07-AOP367

Subjects:
Primary: 60G40 , 91A15 , 93E20
Secondary: 60G44 , 91A25

Keywords: control , Doob–Meyer decompositions , Martingales , Optimal stopping , Stochastic games , stochastic maximum principle , thrifty control strategies

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • July 2008
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