Applied Mathematics & Optimization

, Volume 70, Issue 2, pp 253–278 | Cite as

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

  • Mingshang Hu
  • Shaolin Ji
  • Shuzhen Yang


In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by \(G\)-Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton–Jacobi–Bellman (HJB) equation in the framework of \(G\)-expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.


\(G\)-expectation Backward stochastic differential equations  Stochastic optimal control Dynamic programming principle Viscosity solution 

Mathematics Subject Classification

93E20 60H10 35K15 



We would like to thank S. Peng for many helpful discussions. We also wish to thank the referee for valuable comments.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinan People’s Republic of China
  2. 2.Qilu Institute of FinanceShandong UniversityJinan People’s Republic of China

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