arXiv:2506.07299q-fin.CPcs.LG2025-06被引 1

提出一种无需依赖具体模型的金融优化鲁棒方法,有效应对数据有限下的模型不确定性。

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling

  • 通过引入不确定性度量,对多种模型进行采样评估以增强决策鲁棒性
  • 在真实多期数据中表现优于传统混合模型法,接近贝叶斯方法性能
  • 适合金融风险控制、资产配置等对模型稳定性要求高的场景

本文针对量化金融中因数据有限导致的模型不确定性问题,提出一种模型无关的稳健优化框架。在无法获取真实概率测度的情况下,传统方法依赖经验近似,微小偏差即可能导致决策质量显著下降。基于Klibanoff等(2005)的框架,我们在预期效用或对冲指标等目标上叠加外层不确定性度量,借鉴经典货币风险测度思想。当缺乏自然模型分布或贝叶斯方法不适用时,采用类自助法的子采样策略近似模型不确定性,该策略与深度学习中的小批量采样相关。为解决朴素实现带来的二次内存开销,提出可高效并行化的改进随机梯度下降算法。通过解析、模拟及实证研究(包括多期、真实数据与高维情形),验证了不确定性度量优于传统混合测度策略,且所提子采样方法不仅提升对模型风险的鲁棒性,性能亦可媲美更复杂的贝叶斯方法。

原文摘要 · Abstract (English)

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional objective - whether this is expected utility in an investing context or a hedging metric - by superimposing an outer "uncertainty measure", motivated by traditional monetary risk measures, on the space of models. In scenarios where a natural model distribution is lacking or Bayesian methods are impractical, we propose an ad hoc subsampling strategy, analogous to bootstrapping in statistical finance and related to mini-batch sampling in deep learning, to approximate model uncertainty. To address the quadratic memory demands of naive implementations, we also present an adapted stochastic gradient descent algorithm that enables efficient parallelization. Through analytical, simulated, and empirical studies - including multi-period, real data and high-dimensional examples - we demonstrate that uncertainty measures outperform traditional mixture of measures strategies and our model-agnostic subsampling-based approach not only enhances robustness against model risk but also achieves performance comparable to more elaborate Bayesian methods.

金融优化模型不确定性鲁棒性

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