# Deep-MKV-TS: Path-Dependent McKean--Vlasov Control for Financial Time Series Generation

arXiv: https://arxiv.org/abs/2608.19394 · HTML: https://mlsanity.com/paper/2608.19394/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Deep Latent State Space Models for Time-Series Generation](https://mlsanity.com/paper/2212.12749/) (2022)
- [A mean-field games laboratory for generative modeling](https://mlsanity.com/paper/2304.13534/) (2023)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [Robust time series generation via Schr"odinger Bridge: a comprehensive evaluation](https://mlsanity.com/paper/2503.02943/) (2025)
- [Optimal Execution with Reinforcement Learning](https://mlsanity.com/paper/2411.06389/) (2024)
- [Reinforcement Learning in Queue-Reactive Models: Application to Optimal Execution](https://mlsanity.com/paper/2511.15262/) (2025)
- [Schr"odinger bridge with transport relaxation](https://mlsanity.com/paper/2602.08118/) (2026)
- [Entropic Semi-Martingale Optimal Transport](https://mlsanity.com/paper/2408.09361/) (2024)
- [SBBTS: A Unified Schr"odinger-Bass Framework for Synthetic Financial Time Series](https://mlsanity.com/paper/2604.07159/) (2026)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)

## Abstract (arXiv)

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.