Singular mean-field control games

Yaozhong Hu 1 Bernt Øksendal 2 Agnès Sulem 3
3 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique.
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Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2017, 35 (5), pp.823 - 851. 〈10.1080/07362994.2017.1325745〉
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Yaozhong Hu, Bernt Øksendal, Agnès Sulem. Singular mean-field control games. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2017, 35 (5), pp.823 - 851. 〈10.1080/07362994.2017.1325745〉. 〈hal-01614747〉

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