Viscosity solutions for controlled McKean-Vlasov jump-diffusions

Matteo Burzoni; Vincenzo Ignazio; A. Max Reppen; H. M. Soner

doi:10.1137/19M1290061

Viscosity solutions for controlled McKean-Vlasov jump-diffusions

Matteo Burzoni, Vincenzo Ignazio, A. Max Reppen, H. M. Soner

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1676-1699
Number of pages	24
Journal	SIAM Journal on Control and Optimization
Volume	58
Issue number	3
DOIs	https://doi.org/10.1137/19M1290061
State	Published - 2020

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

Keywords

McKean-Vlasov control
Optimal control
Viscosity solutions
Wasserstein space

Access to Document

10.1137/19M1290061

Cite this

@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 = "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",

}

TY - JOUR

T1 - Viscosity solutions for controlled McKean-Vlasov jump-diffusions

AU - Burzoni, Matteo

AU - Ignazio, Vincenzo

AU - Reppen, A. Max

AU - Soner, H. M.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - McKean-Vlasov control

KW - Optimal control

KW - Viscosity solutions

KW - Wasserstein space

UR - http://www.scopus.com/inward/record.url?scp=85091343847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85091343847&partnerID=8YFLogxK

U2 - 10.1137/19M1290061

DO - 10.1137/19M1290061

M3 - Article

AN - SCOPUS:85091343847

SN - 0363-0129

VL - 58

SP - 1676

EP - 1699

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 3

ER -

Viscosity solutions for controlled McKean-Vlasov jump-diffusions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this