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Dynamic programming principle for stochastic recursive optimal control problem with delayed systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1005-1026

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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.

DOI : 10.1051/cocv/2011187
Classification : 49L20, 60H10, 93E20
Keywords: stochastic differential equation with delay, recursive optimal control problem, dynamic programming principle, Hamilton-Jacobi-Bellman equation 
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     author = {Chen, Li and Wu, Zhen},
     title = {Dynamic programming principle for stochastic recursive optimal control problem with delayed systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1005--1026},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {4},
     year = {2012},
     doi = {10.1051/cocv/2011187},
     mrnumber = {3019470},
     zbl = {1259.49040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011187/}
}
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Chen, Li; Wu, Zhen. Dynamic programming principle for stochastic recursive optimal control problem with delayed systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1005-1026. doi: 10.1051/cocv/2011187

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