Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
Résumé
This paper aims to study the relationship between the maximum principle (MP) and the dynamic programming principle (DPP) for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and the value function can be non-smooth. By making use the notions of the super-, sub-differentials and the conditional expected operator-valued BSIEs, we establish the connection between the first and second-order adjoint variables in MP and the value funtion in DPP. Moreover, the discussions in the smooth case are also presented.
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