Chen, Li; Wu, Zhen Dynamic programming principle for stochastic recursive optimal control problem with delayed systems. (English) Zbl 1259.49040 ESAIM, Control Optim. Calc. Var. 18, No. 4, 1005-1026 (2012). 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. Cited in 10 Documents 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 Keywords:stochastic differential equation with delay; recursive optimal control problem; dynamic programming principle; Hamilton-Jacobi-Bellman equation PDFBibTeX XMLCite \textit{L. Chen} and \textit{Z. Wu}, ESAIM, Control Optim. Calc. Var. 18, No. 4, 1005--1026 (2012; Zbl 1259.49040) Full Text: DOI