Optimal Stopping under Adverse Nonlinear Expectation and Related Games
نویسندگان
چکیده
We study the existence of optimal actions in a zero-sum game infτ supP E P [Xτ ] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem infτ E(Xτ ) for a class of sublinear expectations E(·) such as the G-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope Y and prove that the first hitting time inf{t : Yt = Xt} is an optimal stopping time. The existence of a saddle point is shown under a compactness condition. Finally, the results are applied to the subhedging of American options under volatility uncertainty.
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