带脉冲、预先承诺与无限制成本函数的零和随机微分博弈
A zero-sum stochastic differential game with impulses, precommitment, and unrestricted cost functions
AI总结：
本文研究带脉冲与随机控制的零和随机微分博弈，通过有限值停时的动态规划原理，在无成本递减假设下证明了博弈值的存在性及相应拟变分不等式粘性解的唯一性。
摘要：
我们研究了一个零和随机微分博弈（SDG），其中一方控制者执行脉冲控制，而其对手则执行随机控制。我们考虑了一个不对称的设定，在该设定中，脉冲玩家在博弈开始时承诺执行少于 q 次脉冲（q 可以任意大）。为了获得值函数的均匀连续性，先前涉及带脉冲的 SDG 的工作假设脉冲成本随时间递减。我们的工作通过使用具有有限值停时的动态规划原理来避免此类限制。我们证明了由此产生的博弈具有一个值，进而证明了相关的 Hamilton-Jacobi-Bellman-Isaacs 拟变分不等式粘性解的存在性和唯一性。
英文摘要：
We study a zero-sum stochastic differential game (SDG) in which one controller plays an impulse control while their opponent plays a stochastic control. We consider an asymmetric setting in which the impulse player commits to, at the start of the game, performing less than $q$ impulses ($q$ can be chosen arbitrarily large). In order to obtain the uniform continuity of the value functions, previous works involving SDGs with impulses assume the cost of an impulse to be decreasing in time. Our work avoids such restrictions by using a dynamic programming principle with finite-valued stopping times. We establish that the resulting game admits a value, and in turn, the existence and uniqueness of viscosity solutions to an associated Hamilton-Jacobi-Bellman-Isaacs quasi-variational inequality.
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