Second-Order Necessary Conditions for Optimal Control with Recursive Utilities

  • Yuchao Dong
  • Qingxin MengEmail author


The necessary conditions for an optimal control of a stochastic control problem with recursive utilities are investigated. The first-order condition is the well-known Pontryagin-type maximum principle. When such a first-order necessary condition is singular in some sense, certain type of the second-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.


Recursive optimal control Maximum principle Variation equation Adjoint processes 

Mathematics Subject Classification

49J53 49K45 60H99 



The first author gratefully acknowledges financial support from Région Pays de la Loire through the Grant PANORisk. The second author was supported by the Natural Science Foundation of Zhejiang Province for Distinguished Young Scholar (No. LR15A010001) and the National Natural Science Foundation of China (Nos. 11871211, 11471079). Both authors would like to thank the editors and anonymous reviewers for their valuable comments and suggestions that helped improve the quality of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LAREMA, Départment de MathématiquesUniversité d’AngersAngers Cedex 01France
  2. 2.Department of Mathematical SciencesHuzhou UniversityHuzhouChina

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