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Stochastic verification theorems within the framework of viscosity solutions. (English) Zbl 0880.93059
The authors present the verification theorem for an optimal control problem of diffusion processes in terms of superdifferentials of a viscosity solution to the corresponding Hamilton-Jacobi-Bellman equation. The optimal feedback controls are obtained by maximizing the generalized Hamiltonians over both the control domains and the superdifferentials of the payoff function.

MSC:
93E20Optimal stochastic control (systems)
49L20Dynamic programming method (infinite-dimensional problems)
49L25Viscosity solutions (infinite-dimensional problems)