Singular mean-field control games with applications to optimal harvesting and investment problems

2014/06/07 by Yaozhong Hu, Hu, Yaozhong, Bernt Øksendal +3
Mathematics · #60H10 #91A15 #91A23 #91B38 #91B55 #91B70 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:60H10 #msc:91A15 #msc:91A23 #msc:91B38 #msc:91B55 #msc:91B70 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1406.1863

arxiv created 2014/06/07 · arxiv updated 2014/06/10

Abstract

This paper studies singular mean field control problems and singular mean field 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. Applications are given to optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and to 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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