Parabolic Bellman equations with risk control

Dominic Breit, Jens Frehse, Alain Bensoussan

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We 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.
Original languageEnglish
Pages (from-to)1535–1549
Number of pages15
JournalSIAM Journal on Control and Optimization
Issue number2
Publication statusPublished - 17 Apr 2018


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