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<p>In the financial system, bailout strategies play a pivotal role in mitigating substantial losses resulting from systemic risk. However, the lack of a closed-form objective function to the optimal bailout problem poses significant challenges in its resolution. This paper conceptualizes the optimal bailout (capital injection) problem as a black-box optimization task, where the black box is modeled as a fixed-point system consistent with the E–N framework for measuring systemic risk in the financial system. To address this challenge, we propose a novel framework, “Prediction-Gradient-Optimization” (PGO). Within PGO, the <i>Prediction</i> employs a neural network to approximate and forecast the objective function implied by the black box, which can be completed offline; for the online usage, the <i>Gradient</i> step derives gradient information from this approximation, and the <i>Optimization</i> step uses a gradient projection algorithm to solve the problem effectively. Extensive numerical experiments highlight the effectiveness of the proposed approach in managing systemic risk.</p>

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Optimal Bailout for Systemic Risk: A PGO Approach Based on Neural Network

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Shu-Hua Xiao,
  • Jia-Li Ma,
  • Li Xia,
  • Shu-Shang Zhu

摘要

In the financial system, bailout strategies play a pivotal role in mitigating substantial losses resulting from systemic risk. However, the lack of a closed-form objective function to the optimal bailout problem poses significant challenges in its resolution. This paper conceptualizes the optimal bailout (capital injection) problem as a black-box optimization task, where the black box is modeled as a fixed-point system consistent with the E–N framework for measuring systemic risk in the financial system. To address this challenge, we propose a novel framework, “Prediction-Gradient-Optimization” (PGO). Within PGO, the Prediction employs a neural network to approximate and forecast the objective function implied by the black box, which can be completed offline; for the online usage, the Gradient step derives gradient information from this approximation, and the Optimization step uses a gradient projection algorithm to solve the problem effectively. Extensive numerical experiments highlight the effectiveness of the proposed approach in managing systemic risk.