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arXiv · 1909.12337

Viscosity solutions for controlled McKean--Vlasov jump-diffusions

Matteo Burzoni·Vincenzo Ignazio·A. Max Reppen·H. Mete Soner
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Abstract

We study a class of non linear integro-differential equations on the Wasserstein space 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 an Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution.

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Matteo Burzoni, Vincenzo Ignazio, A. Max Reppen, H. Mete Soner. 2019-09-26. Viscosity solutions for controlled McKean--Vlasov jump-diffusions. https://arxiv.org/abs/1909.12337

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