Journal of Optimization Theory and Applications

, Volume 179, Issue 2, pp 501–532 | Cite as

Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

  • Yan Wang
  • Lei WangEmail author
  • Kok Lay Teo


We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.


Necessary optimality conditions Sufficient optimality conditions Regular–singular control Stochastic differential game Asymmetric information Saddle point Nash equilibrium Optimal investment Dividend Model uncertainty 

Mathematics Subject Classification

91G80 91A15 91A23 93E20 60J75 91B28 91B30 



This work was supported by the National Natural Science Foundation for the Youth of China (Grants 11701064, 11301081, 11401073), the Science Research Project of Educational Department of Liaoning Province of China (Grants L2014188, L2015097 and L2014186), the Fundamental Research Funds for Central Universities in China (Grant DUT15LK25), and the Research Funding for Doctor Start-Up Program of Liaoning Province (Grant 201601245).


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Authors and Affiliations

  1. 1.School of ScienceDalian Jiaotong UniversityDalianChina
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianChina
  3. 3.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia

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