Martingale approach to stochastic differential games of control and stopping

Details Martingale approach to stochastic differential games of control and stopping Martingale approach to stochastic differential games of control and stopping

2008-08-27

arxiv.org/abs/0808.3656v1

Annals of Probability 2008, Vol. 36, No. 4, 1495-1527

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP367 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP367

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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