# Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 1005-1026
- ISSN: 1292-8119

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topChen, Li, and Wu, Zhen. "Dynamic programming principle for stochastic recursive optimal control problem with delayed systems." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1005-1026. <http://eudml.org/doc/272946>.

@article{Chen2012,

abstract = {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.},

author = {Chen, Li, Wu, Zhen},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {stochastic differential equation with delay; recursive optimal control problem; dynamic programming principle; Hamilton-Jacobi-Bellman equation},

language = {eng},

number = {4},

pages = {1005-1026},

publisher = {EDP-Sciences},

title = {Dynamic programming principle for stochastic recursive optimal control problem with delayed systems},

url = {http://eudml.org/doc/272946},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Chen, Li

AU - Wu, Zhen

TI - Dynamic programming principle for stochastic recursive optimal control problem with delayed systems

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 4

SP - 1005

EP - 1026

AB - 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.

LA - eng

KW - stochastic differential equation with delay; recursive optimal control problem; dynamic programming principle; Hamilton-Jacobi-Bellman equation

UR - http://eudml.org/doc/272946

ER -

## References

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- [12] Z. Wu and Z. Yu, Dynamic programming principle for one kind of stochastic recursive optimal control problem and Hamilton-Jacobi-Bellman equation. SIAM J. Control Optim.47 (2008) 2616–2641. Zbl1171.49022MR2452889
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