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

Li Chen; Zhen Wu

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

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

Abstract

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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.

How to cite

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Chen, 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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  10. [10] S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellmen equation. Stoch. Stoch. Rep.38 (1992) 119–134. Zbl0756.49015MR1274898
  11. [11] S. Peng, Backward stochastic differential equations-stochastic optimization theory and viscosity solution of HJB equations. Topics on Stochastic Analysis (in Chinese), edited by J. Yan, S. Peng, S. Fang and L. Wu. Science Press, Beijing (1997) 85–138. 
  12. [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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