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arXiv · 0808.3656

Martingale approach to stochastic differential games of control and stopping

Ioannis Karatzas·Ingrid-Mona Zamfirescu
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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. 2008-08-27. Martingale approach to stochastic differential games of control and stopping. https://doi.org/10.1214/07-aop367

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