Mean field capital accumulation with stochastic depreciation

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.