This work is concerned with the modeling and analysis of continuous time mean field capital accumulation optimization. We begin by considering a mean field generalization of the so-called AK model combined with HARA utility. This model allows explicit calculation of the local strategy and the determination of the closed-loop mean field dynamics and the asymptotic property. The next part introduces a nonlinear model addressing diminishing return to scale. The mean field game is examined by use of the HJB equation. When the Cobb-Douglas production function and HARA utility are used, the solution of the mean field game is calculated by a set of ordinary differential equations, which is useful from the computational point of view since one can avoid implicitly determining the control by partial differential equations.

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Conference 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Huang, M, & Nguyen, S.L. (Son Luu). (2014). Mean field capital accumulation with stochastic depreciation. In Proceedings of the IEEE Conference on Decision and Control (pp. 370–375). doi:10.1109/CDC.2014.7039409