@article{a8cabda736b94156a2e2bfbf3fb78a60,
title = "Viscosity solutions for controlled McKean-Vlasov jump-diffusions",
abstract = "We study a class of nonlinear integrodifferential equations on a subspace of all probability measures on the real line 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 a Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution.",
keywords = "McKean-Vlasov control, Optimal control, Viscosity solutions, Wasserstein space",
author = "Matteo Burzoni and Vincenzo Ignazio and Reppen, {A. Max} and Soner, {H. M.}",
note = "Funding Information: \ast Received by the editors September 27, 2019; accepted for publication (in revised form) April 26, 2020; published electronically June 23, 2020. https://doi.org/10.1137/19M1290061 Funding: The first author was partly supported by the Hooke Research Fellowship from the University of Oxford. The third author was supported by the Swiss National Science Foundation grant SNF 181815. The first, second, and fourth authors were partly supported by the Swiss National Science Foundation grant SNF 200020 172815. The fourth author was partly supported by the ETH Foundation and the Swiss Finance Institute. \dagger Mathematical Institute, University of Oxford, Oxford, UK (matteo.burzoni@maths.ox.ac.uk). \ddagger Department of Mathematics, ETH, Zu\{"}rich, 8092, Switzerland (vincenzo.ignazio@math.ethz.ch). \S Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08540 (areppen@princeton.edu, soner@princeton.edu). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/19M1290061",
language = "English (US)",
volume = "58",
pages = "1676--1699",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}