“神经网络在金融决策中担任的角色”系列文献研读——孔文鹏分享

科研基地组织前沿文献研读交流会，孔文鹏主要围绕两篇运筹学与金融决策交叉领域的前沿论文进行主题分享：一篇为2026年发表于中国运筹学会会刊Journal of the Operations Research Society of China的Optimal Bailout for Systemic Risk: A PGO Approach Based on Neural Network；另一篇为2024年发表于Springer旗下运筹学主流期刊Annals of Operations Research的End-to-End Risk Budgeting Portfolio Optimization with Neural Networks。

在金融决策领域，神经网络扮演着多元化的计算角色，主要可归纳为四种：预测器、目标代理、优化层与直接策略。预测器是最常见且基础的角色，负责利用历史数据预测未来结果或估计参数，再交由规则或优化器生成决策（因其普及性，本次分享不展开赘述）；目标代理则通过神经网络近似替代高成本的方案评价；优化层将显式目标与约束保留在优化问题中，通过网络反向传播训练参数；直接策略则是端到端地学习从信息到行动的映射，直接生成决策。基于这一角色框架，本次文献研读将重点分享两篇运筹学与金融决策交叉领域的前沿论文：第一篇（Optimal Bailout for Systemic Risk）主要对应“目标代理”角色，利用神经网络拟合黑箱目标函数以解决系统性风险最优救助问题；第二篇（End-to-End Risk Budgeting Portfolio Optimization）则涉及“优化层”与“直接策略”后两个角色，探讨了端到端的投资组合优化模型。

第一篇论文关注银行系统性风险中的最优救助问题。在金融体系中，救助策略对于缓解由系统性风险引起的巨额损失起着关键作用。然而，最优救助问题不存在闭式目标函数，给该问题的求解带来了重大挑战。本文将最优救助（注资）问题抽象为一个黑箱优化任务，其中该黑箱被建模为一个不动点系统，该系统与用于度量金融体系系统性风险的E–N框架相一致。针对这一难题，文章提出了一个新型框架——“预测-梯度-优化”（PGO）。在PGO框架内，预测阶段利用神经网络对黑箱所隐含的目标函数进行拟合和预测，该环节可离线完成；在线应用时，梯度环节基于该近似结果提取梯度信息，优化环节则采用梯度投影算法高效求解问题。大量数值实验表明，该方法在系统性风险管控方面具备良好效果。

ABSTRACT

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.

第二篇论文关注传统两步法组合优化的误差问题。投资组合优化一直是金融领域的一个核心问题，通常采用两步法解决：先校准参数，然后求解优化问题。然而，这种两步法有时会遇到“误差最大化”问题，即参数估计的偏差会导致不合理的资产配置决策。本文将预测和优化任务整合到一个前馈神经网络中，采用端到端的建模思路，直接从输入特征中学习投资组合配置权重。本文构建了两类端到端投资组合模型：无模型网络与基于模型的网络。无模型方法被视为黑箱，而基于模型的方法会学习各资产的最优风险贡献，并通过嵌入神经网络的隐式优化层来完成资产配置。当以最大化夏普比率作为训练目标函数时，基于模型的端到端框架在样本外（2017-2021年）测试中表现稳健夏普比率可达1.16；作为对照，标准风险平价策略夏普比率为0.79，等权重固定混合策略为0.83。考虑到基于风险的投资组合对底层资产池较为敏感，本文在神经网络中引入带随机门控的资产筛选机制，避免组合被低收益、低波动资产拖累。带筛选门控的端到端模型性能优于采用简单筛选机制的标准风险平价基准，使样本外期间（2017-2021年）的市场数据中夏普比率提升至1.24。

ABSTRACT

Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the “error maximization” problem where inaccuracy in parameter estimation translates to unwise allocation decisions. In this paper, we combine the prediction and optimization tasks in a single feed-forward neural network and implement an end-to-end approach, where we learn the portfolio allocation directly from the input features. Two end-to-end portfolio constructions are included: a model-free network and a model-based network. The model-free approach is seen as a black-box, whereas in the model-based approach, we learn the optimal risk contribution on the assets and solve the allocation with an implicit optimization layer embedded in the neural network. The model-based end-to-end framework provides robust performance in the out-of-sample (2017-2021) tests when maximizing Sharpe ratio is used as the training objective function, achieving a Sharpe ratio of 1.16 when nominal risk parity yields 0.79 and equal-weight fix-mix yields 0.83. Noticing that risk-based portfolios can be sensitive to the underlying asset universe, we develop an asset selection mechanism embedded in the neural network with stochastic gates, in order to prevent the portfolio being hurt by the low-volatility assets with low returns. The gated end-to-end with filter outperforms the nominal risk-parity benchmarks with naive filtering mechanism, boosting the Sharpe ratio of the out-of-sample period (2017-2021) to 1.24 in the market data.