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

35 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

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10.1137/19M1290061

Cite this

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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.\}",

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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

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UR - https://www.scopus.com/pages/publications/85091343847#tab=citedBy

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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

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