Deep-MKV-TS：用于金融时间序列生成的路径依赖型McKean-Vlasov控制

中文摘要 AI 辅助

我们提出了Deep-MKV-TS，一种用于金融场景生成的路径依赖型McKean-Vlasov框架。该随机动力学通过将生成场景的选定路径特征和波动率特征与数据中观测到的对应特征进行匹配来确定。从可解释的参考模型出发，Deep-MKV-TS保留参考模型的漂移项并调整其波动率，同时正则化惩罚项限制其与校准后动力学的不必要偏离。我们采用基于样本的随机最大值原理的神经实现来求解所得的控制问题。我们针对可精确计算的基准模型验证了该方法。在Heston模型和Heston混合模型上，Deep-MKV-TS大幅降低了参考模型的路径依赖型缺陷和波动率相关缺陷。在延迟波动率实验中，随着预测 horizon（预测时域）的增加，校正效果仍然有效，而直接训练的可靠性则下降。在保留的日内股票指数期货数据上，校正后的模型相较于参考模型改进了条件预测性能，达到了与灵活生成基线和历史基线相当的性能水平。在固定回撤风险目标下，生成的场景也支持比参考模型更高的风险敞口。这些结果表明，路径依赖型McKean-Vlasov控制可在不替换可解释参考模型的前提下对其进行增强。

英文摘要

We introduce Deep-MKV-TS, a path-dependent McKean-Vlasov framework for financial scenario generation. The stochastic dynamics are chosen by matching selected path and volatility features of generated scenarios to those observed in the data. Starting from an interpretable reference model, Deep-MKV-TS preserves the reference drift and adjusts its volatility, while a regularization penalty limits unnecessary departures from the calibrated dynamics. We solve the resulting control problem using a neural, sample-based implementation of the stochastic maximum principle. We validate the method against an exactly computable oracle. On Heston and Heston-mixture models, Deep-MKV-TS substantially reduces path-dependent and volatility-related deficiencies of the reference model. In delayed-volatility experiments, the correction remains effective as the forecasting horizon increases, while direct training becomes less reliable. On held-out intraday equity-index futures, the corrected model improves conditional forecasts relative to the reference and reaches a level of performance comparable to flexible generative and historical baselines. The resulting scenarios also support greater exposure than the reference under a fixed drawdown-risk target. These results show that path-dependent McKean-Vlasov control can enrich an interpretable reference model without replacing it.

发表机构

• Murex SAS（穆雷克斯公司）
• École Polytechnique（巴黎综合理工学院）
• BNP-PAR（法国巴黎银行）

机构由 AI 辅助整理，请以论文原文为准。