arXiv：cs.LG· Andrea Della Vecchia, Damir Filipovi\'c·· 5 小时前AI 评分29
动态规划中的误差传播：从随机控制到美式期权定价
Error Propagation in Dynamic Programming: From Stochastic Control to American Option Pricing
AI 导读
该论文为离散时间随机最优控制（SOC）建立理论与方法基础，用非参数回归结合 Monte Carlo 子采样估计值函数，回归在 RKHS 中通过 KRR 算法完成。作者提出误差分解并逐时间步严格控制误差项，进而分析误差如何从到期日向初始阶段反向传播。该分析被应用于美式期权定价，论文已被 ICML 2026 接收。
正文
Abstract:This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.
| Comments: | Accepted to the 43rd International Conference on Machine Learning, Seoul, South Korea, 2026 |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Computational Finance (q-fin.CP); Pricing of Securities (q-fin.PR); Applications (stat.AP) |
| Cite as: | arXiv:2509.20239 [stat.ML] |
| (or arXiv:2509.20239v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2509.20239 arXiv-issued DOI via DataCite |
Submission history
From: Andrea Della Vecchia [view email]
[v1]
Wed, 24 Sep 2025 15:30:19 UTC (446 KB)
[v2]
Fri, 2 Oct 2026 11:58:21 UTC (444 KB)
来源：arXiv：cs.LG · arxiv.org