High-dimensional stochastic control models for newsvendor problems and deep learning resolution
研究了动态补货、金融对冲和Stackelberg竞争同时存在的报童问题，建立高维随机控制模型，用深度学习算法求解高维HJB方程，数值结果验证了算法精度和风险缓解效果。
Abstract This paper studies continuous-time models for newsvendor problems with dynamic replenishment, financial hedging and Stackelberg competition. These factors are considered simultaneously and the high-dimensional stochastic control models are established. High-dimensional Hamilton-Jacobi-Bellman (HJB) equations are derived for the value functions. To circumvent the curse of dimensionality, a deep learning algorithm is proposed to solve the HJB equations. A projection is introduced in the algorithm to avoid the gradient explosion during the training phase. The deep learning algorithm is implemented for HJB equations derived from the newsvendor models with dimensions up to six. Numerical outcomes validate the algorithm’s accuracy and demonstrate that the high-dimensional stochastic control models can successfully mitigate the risk.