Linear-quadratic optimal control problems for mean-field stochastic differential equations — time-consistent solutions

Yong, Jiongmin

doi:10.1090/tran/6502

Linear-quadratic optimal control problems for mean-field stochastic differential equations — time-consistent solutions
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Trans. Amer. Math. Soc. 369 (2017), 5467-5523 Request permission

Abstract:

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kinds of problems. Open-loop solutions are presented by means of the variational method with decoupling of forward-backward stochastic differential equations, which leads to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which leads to a Riccati equation system with a symmetric structure.

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