We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard $(I-1)$-simplex which represents the probabilities with which the $I$ possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.

翻译：本文提出了一种可实现的、基于神经网络的结构保持概率数值逼近方法，用于求解描述具有非对称信息的零和最优停止微分博弈价值的广义障碍问题。目标解依赖于三个变量：时间变量、空间（或状态）变量，以及来自标准$(I-1)$-单纯形的变量——该变量表示博弈$I$种可能配置的进行概率。所提出的数值逼近方法保持了连续解的凸性以及上下障碍边界。我们证明了全离散格式收敛于连续问题唯一黏性解，并通过一系列数值实验展示了该方法的适用性。