论文标题
零和零奇数控制器与塞子游戏的无界域上的差异不平等
Variational inequalities on unbounded domains for zero-sum singular-controller vs. stopper games
论文作者
论文摘要
我们在有限的时间范围内研究了一个奇异控制器和塞子之间的一类零和游戏。基础过程是在无限域中演变的多维（局部非脱位）随机微分方程（SDE）。我们证明，这样的游戏承认了一个价值，并为塞子提供了最佳的策略。在合适的Sobolev类中，该游戏的值被证明是具有障碍物约束和梯度约束的“ Min-Max”类型的各种不平等的最大解决方案。尽管变异不等式和游戏是在无限域中解决的，但我们不需要受控SDE的系数或游戏中的成本功能的界限。
We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an unbounded domain. We prove that such games admit a value and provide an optimal strategy for the stopper. The value of the game is shown to be the maximal solution, in a suitable Sobolev class, of a variational inequality of `min-max' type with obstacle constraint and gradient constraint. Although the variational inequality and the game are solved on an unbounded domain we do not require boundedness of either the coefficients of the controlled SDE or of the cost functions in the game.
