For mean-field type control problems, stochastic dynamic programming requires adaptation. We propose to reformulate the problem as a distributed control problem by assuming that the PDF $\rho$ of the stochastic process exists. Then we show that Bellman's principle applies to the dynamic programming value function $V(\tau,\rho_\tau)$ where the dependency on $\rho_\tau$ is functional as in P.L. Lions' analysis of mean-filed games (2007). We derive HJB equations and apply them to two examples, a portfolio optimization and a systemic risk model.