Parabolic Bellman-Systems with Mean Field Dependence

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)419-432
Journal / PublicationApplied Mathematics and Optimization
Volume73
Issue number3
Publication statusPublished - 1 Jun 2016

Abstract

We consider the necessary conditions for Nash-points of Vlasov-McKean functionals Ji[v]=∫Qmfi(·,m,v)dxdt (i= 1 ,.. , N). The corresponding payoffs fi depend on the controls v and, in addition, on the field variable m= m(v). The necessary conditions lead to a coupled forward-backward system of nonlinear parabolic equations, motivated by stochastic differential games. The payoffs may have a critical nonlinearity of quadratic growth and any polynomial growth w.r.t. m is allowed as long as it can be dominated by the controls in a certain sense. We show existence and regularity of solutions to these mean-field-dependent Bellman systems by a purely analytical approach, no tools from stochastics are needed.

Research Area(s)

  • Bellman equations, Mean field dependence, Nonlinear parabolic systems, Stochastic differential games

Citation Format(s)

Parabolic Bellman-Systems with Mean Field Dependence. / Bensoussan, Alain; Breit, Dominic; Frehse, Jens.
In: Applied Mathematics and Optimization, Vol. 73, No. 3, 01.06.2016, p. 419-432.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review