Zero-sum stochastic differential games of generalized McKean-Vlasov type *

Abstract : We study zero-sum stochastic differential games where the state dynamics of the two players is governed by a generalized McKean-Vlasov (or mean-field) stochastic differential equation in which the distribution of both state and controls of each player appears in the drift and diffusion coefficients, as well as in the running and terminal payoff functions. We prove the dynamic programming principle (DPP) in this general setting, which also includes the control case with only one player, where it is the first time that DPP is proved for open-loop controls. We also show that the upper and lower value functions are viscosity solutions to a corresponding upper and lower Master Bellman-Isaacs equation. Our results extend the seminal work of Fleming and Souganidis [15] to the McKean-Vlasov setting.
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Soumis le : dimanche 18 mars 2018 - 19:13:23
Dernière modification le : lundi 18 mars 2019 - 16:03:41
Document(s) archivé(s) le : mardi 11 septembre 2018 - 09:13:56


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  • HAL Id : hal-01736890, version 1
  • ARXIV : 1803.07329


Huyen Pham, Andrea Cosso. Zero-sum stochastic differential games of generalized McKean-Vlasov type *. 2018. 〈hal-01736890〉



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