本项目旨在利用 Bellman 动态规划方法研究控制集无界的几类随机微分对策问题及相应的 Hamilton-Jacobi 方程的粘性解的存在唯一性。在允许控制集无界的情况下，并且相应的 Hamilton 函数不具有凸性或凹性时，开展如下研究：(i) 二人零和随机微分对策问题相应的 Hamilton-Jacobi 方程的粘性解的存在唯一性，并在 Isaacs 条件成立时，建立随机微分对策问题值函数的存在性；(ii) 具有反射障碍的二人零和随机微分对策问题及相应的具有障碍算子的 Isaacs 方程的粘性解的存在唯一性。最后将研究结果与经典情形比较，并举例说明本项目拟研究问题的先进性。

This project intends to study several stochastic differential games with unbounded controls by using Bellman's dynamic programming principle. All the arguments of this project will be carried out with the unbounded control domains and without relying on the convexity or concavity of the corresponding Hamiltonians. We will investigate the jobs on the following aspects: (i) The existence and uniqueness of the viscosity solutions to upper and lower Hamilton-Jacobi equations respectively, which corresponding to two-person zero-sum stochastic differential games. To get the existence of the value function of such stochastic differential games under the Isaacs condition. (ii) The existence and uniqueness of the viscosity solutions to upper and lower Isaacs equations with obstacle respectively, which corresponding to two-person zero-sum stochastic differential games with reflection and related obstacle. To get the existence of the value function of such stochastic differential games. Then we will give a comparison between our conclusions and the classical results. Also, some examples will be given to show that the problems of this project are sharp in some sense.