Articlediamond2015

A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon

121 citations0/0 files storedMathematical Control and Related Fields

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Stochastic processes and financial applications Stability and Control of Uncertain Systems Stability and Controllability of Differential Equations

Abstract

A linear-quadratic (LQ, for short) optimal control problem is consideredfor mean-field stochastic differential equations with constantcoefficients in an infinite horizon. The stabilizability of thecontrol system is studied followed by the discussion of thewell-posedness of the LQ problem. The optimal control can beexpressed as a linear state feedback involving the state and itsmean, through the solutions of two algebraic Riccati equations. Thesolvability of such kind of Riccati equations is investigated bymeans of semi-definite programming method.

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References

2007Mean field games 1999Stochastic controls : Hamiltonian systems and HJB equations 2006Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle 1999Stochastic Controls 2009Mean-field backward stochastic differential equations and related partial differential equations 2013Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations 2010A Maximum Principle for SDEs of Mean-Field Type 2009Mean-field backward stochastic differential equations: A limit approach

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