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A study on optimal control problem with \(\varepsilon ^{\lambda }-\)error bound for stochastic systems with application to linear quadratic problem

  • Samira Boukaf
  • Mokhtar Hafayed
  • Messaoud Ghebouli
Article
  • 48 Downloads

Abstract

In this paper, we study near-optimal stochastic control problem with \(\varepsilon ^{\lambda }-\)error bound for systems governed by nonlinear controlled Itô stochastic differential equations. The control is allowed to enter into both drift and diffusion coefficients and the control domain need be convex. The proof of our main result is based on Ekeland’s variational principle and some approximation arguments on the state variable and adjoint process with respect to the control variable. Finally, as an example, the linear quadratic control problem is given to illustrate our theoretical results.

Keywords

Stochastic control with \(\varepsilon ^{\lambda }-\)error bound Weak maximum principle Necessary and sufficient of conditions of near-optimality Ekeland’s variational principle  Convex perturbation 

Mathematics Subject Classification

93E20 60H10 

Notes

Acknowledgments

The authors would like to thank two anonymous referees for their constructive and insightful comments for improving the quality of this work.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Samira Boukaf
    • 1
  • Mokhtar Hafayed
    • 2
  • Messaoud Ghebouli
    • 3
  1. 1.Department of EconomicsEl Oued UniversityEl OuedAlgeria
  2. 2.Laboratory of Applied MathematicsBiskra UniversityBiskraAlgeria
  3. 3.Department of MathematicsBordj Bou Arreridj UniversityBordj-Bou-ArreridjAlgeria

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