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Singular mean field control games

Hu, Yaozhong; Øksendal, Bernt; Sulem, Agnès
Journal article; AcceptedVersion; Peer reviewed
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%5BHOS%5D28April2017MeanfieldSingGames.pdf (352.3Kb)
Year
2017
Permanent link
http://urn.nb.no/URN:NBN:no-61024

CRIStin
1493265

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  • Matematisk institutt [2453]
  • CRIStin høstingsarkiv [15984]
Original version
Stochastic Analysis and Applications. 2017, DOI: http://dx.doi.org/10.1080/07362994.2017.1325745
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.

The final version of this research has been published in Stochastic Analysis and Applications. © 2017 Taylor & Francis
 
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