Deep-MKV-TS: Path-Dependent McKean–Vlasov Control for Financial Time Series Generation
Published:
Recommended citation: https://arxiv.org/pdf/2608.19394
Co-authors
Abstract
We introduce Deep-MKV-TS, a path-dependent McKean–Vlasov framework for financial scenario generation. The stochastic dynam- ics 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 refer- ence 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