Viscosity solutions for controlled McKean--Vlasov jump-diffusions
Optimization and Control
2019-10-03 v2 Probability
Abstract
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.
Cite
@article{arxiv.1909.12337,
title = {Viscosity solutions for controlled McKean--Vlasov jump-diffusions},
author = {Matteo Burzoni and Vincenzo Ignazio and A. Max Reppen and H. Mete Soner},
journal= {arXiv preprint arXiv:1909.12337},
year = {2019}
}