High-dimensional stochastic control models for newsvendor problems and deep learning resolution

Jingtang Ma () and Shan Yang ()
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Jingtang Ma: Southwestern University of Finance and Economics
Shan Yang: University of New South Wales

Annals of Operations Research, 2024, vol. 339, issue 1, No 29, 789-811

Abstract: 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.

Keywords: Supply chain management; Newsvendor models; Stochastic control; Dynamic replenishment; Financial hedging; Stackelberg game; Deep learning (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-024-05872-2

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