# Viscosity solutions for controlled McKean--Vlasov jump-diffusions

arXiv: https://arxiv.org/abs/1909.12337 · HTML: https://mlsanity.com/paper/1909.12337/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2019.

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

- [Policy Gradient for Continuous-Time Mean-Field Control](https://mlsanity.com/paper/2605.20718/) (2026)
- [A PDE approach for regret bounds under partial monitoring](https://mlsanity.com/paper/2209.01256/) (2022)

## Abstract (arXiv)

We study a class of non linear integro-differential equations on the Wasserstein space related to the optimal control of McKean--Vlasov jump-diffusions. We develop an intrinsic notion of viscosity solutions that does not rely on the lifting to an Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution.