Stochastic verification theorems within the framework of viscosity solutions. (English) Zbl 0880.93059

Zhou, Xun Yu; Yong, Jiongmin; Li, Xunjing

SIAM J. Control Optimization 35, No. 1, 243-253 (1997).

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.

Reviewer: H.Pragarauskas (Vilnius)

MSC:

93E20	Optimal stochastic control
49L20	Dynamic programming in optimal control and differential games
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games

Keywords:

optimal control of diffusion processes; verification theorem; viscosity solution; Hamilton-Jacobi-Bellman equation; superdifferential