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We consider a jump-diffusion mean field control problem with regime switchingin the state dynamics. The corresponding value function is characterized as theunique viscosity solution of a HJB master equation on the space of probabilitymeasures. Using this characterization, we prove that the value function, whichis not regular, is the limit of a finite agent centralized optimal controlproblem as the number of agents go to infinity, with an explicit convergencerate. Assuming in addition that the value function is smooth, we establish aquantitative propagation of chaos result for the optimal trajectory of agentstates.

Mean field control and finite dimensional approximation for regime-switching jump diffusions