Antonio Ocello (Sorbonne-univ., Paris)
We study the existence of optimal control for branching diffusion processes. The considered problem use rewards that can be nonlinear in the final payoff and linear in the running payout. We give a relaxed formulation, showing its equivalence with the strong problem and proving the existence of optimal controls. Using the dynamic programming principle, we prove that the maximizer can be found in the class of Markovian controls. Finally, we characterize the value function as a viscosity solution of an HJB equation in the space of measures
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