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Dynamic programming principle for stochastic recursive optimal control problem with delayed systems. (English) Zbl 1259.49040

Summary: In this paper, we study one kind of stochastic recursive optimal control problem for the systems described by Stochastic Differential Equations with Delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of optimal control problems and show that the value function is the viscosity solution of the corresponding infinite dimensional Hamilton-Jacobi-Bellman partial differential equation.

MSC:

49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
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