Abstract: We study a finite horizon optimal control problem on McKean-Vlasov branching diffusion processes, in which the interaction term corresponds to the marginal measure induced by the population. Within the framework of closed-loop strategies, we first establish an appropriate dynamic programming principle.  Under further regularity assumption, we prove that the value function satisfies a Hamilton-Jacobi-Bellman equation, which takes the form of a PDE on the space of finite nonnegative measures. We also identify an optimal control in a feedback form by means of a classical verification theorem. We finally illustrate our findings by considering a linear-quadratic example, for which explicit solutions are derived in terms of Riccati equations.

A joint work with Jiazhi Kang, Tianxu Lan and Xiaolu Tan.