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. Read More: https://epubs.siam.org/doi/10.1137/19M1290061
Viscosity solutions for controlled McKean–Vlasov jump-diffusions / M. Burzoni, V. Ignazio, M. Reppen, M. Soner. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 58:3(2020 Jun 23), pp. 1676-1699. [10.1137/19M1290061]
Viscosity solutions for controlled McKean–Vlasov jump-diffusions
M. Burzoni;
2020
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. Read More: https://epubs.siam.org/doi/10.1137/19M1290061
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