标题： 涉及脉冲控制和双障碍拟变分不等式的随机微分博弈 显示英文标题

标题： Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities

摘要： 我们研究一个在有限时间范围内，双方玩家都采用脉冲控制的二人零和随机微分博弈。 该博弈的哈密顿-雅可比-贝尔曼-伊萨克斯（HJBI）偏微分方程实际上是一个双障碍拟变分不等式，因此两个障碍是隐式给出的。 我们证明了上值函数和下值函数是一致的，事实上，我们通过随机微分博弈的动态规划原理，证明它们是HJBI方程的唯一粘性解，从而证明了该博弈存在价值。 显示英文摘要

摘要： We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation of the game turns out to be a double-obstacle quasi-variational inequality, therefore the two obstacles are implicitly given. We prove that the upper and lower value functions coincide, indeed we show, by means of the dynamic programming principle for the stochastic differential game, that they are the unique viscosity solution to the HJBI equation, therefore proving that the game admits a value.