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Martingale approach to stochastic differential games of control and stopping. (English) Zbl 1142.93040
Summary: 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.
93E20Optimal stochastic control (systems)
60G40Stopping times; optimal stopping problems; gambling theory
91A15Stochastic games
91A25Dynamic games
60G44Martingales with continuous parameter
49K45Optimal stochastic control (optimality conditions)