# A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems

arXiv: https://arxiv.org/abs/1803.00445 · HTML: https://mlsanity.com/paper/1803.00445/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise](https://mlsanity.com/paper/2512.14967/) (2025)

## Abstract (arXiv)

We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.