Linear-Quadratic McKean-Vlasov Stochastic Differential Games

Abstract : We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and infinite horizon problems with possibly some random coefficients as well as common noise are addressed. We propose a simple direct approach based on weak martingale optimality principle together with a fixed point argument in the space of controls for solving this game problem. The Nash equilibria are characterized in terms of systems of Riccati ordinary differential equations and linear mean-field backward stochastic differential equations: existence and uniqueness conditions are provided for such systems. Finally, we illustrate our results on a toy example.
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Pré-publication, Document de travail
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Contributeur : Huyen Pham <>
Soumis le : samedi 1 décembre 2018 - 17:37:41
Dernière modification le : mardi 26 mars 2019 - 15:02:50
Document(s) archivé(s) le : samedi 2 mars 2019 - 13:14:59


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  • HAL Id : hal-01941591, version 1
  • ARXIV : 1812.00632


Enzo Miller, Huyen Pham. Linear-Quadratic McKean-Vlasov Stochastic Differential Games. 2018. 〈hal-01941591〉



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