Viscosity solutions for controlled McKean-Vlasov jump-diffusions

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

Research output: Contribution to journalArticlepeer-review

1 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 languageEnglish (US)
Pages (from-to)1676-1699
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume58
Issue number3
DOIs
StatePublished - 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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