Bensoussan, AlainBreit, D.Frehse, J.2019-06-282019-06-282018-04-170363-0129https://hdl.handle.net/10735.1/6641We consider stochastic optimal control problems with an additional term representing the variance of the control functions. The latter one may serve as a risk control. We present and treat the problem in a purely analytical way via a Vlasov-McKean functional and Bellman equations with mean field dependence. We obtain global existence and, essentially, optimal global regularity for the solutions of the Bellman equation and the minimizing control. Surprisingly, the risk term simplifies the analysis to a certain extend.en©2018 Society for Industrial and Applied Mathematics PublicationsMean field theoryLoss controlDynamic programmingRisk assessmentStochastic systemsDifferential equations, ParabolicStochastic differential equationsStochastic control theoryarticleBensoussan, A., D. Breit, and J. Frehse. 2018. "Parabolic bellman equations with risk control." SIAM Journal on Control and Optimization 56(2): 1535-1549.562