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SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 112202(2018) https://doi.org/10.1007/s11432-017-9293-4

A leader-follower stochastic linear quadratic differential game with time delay

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  • ReceivedAug 7, 2017
  • AcceptedNov 6, 2017
  • PublishedMay 21, 2018

Abstract

In this paper, we are concerned with the leader-follower stochastic differentialgame of Itôtype with time delay appearing in the leader's control.The open-loop solution is explicitly given in the form of the conditionalexpectation with respect to several symmetric Riccati equations.The key technique is to establish the nonhomogeneousrelationship between the forward variables and the backward onesobtained in the optimization problems of both the follower and the leader.


Acknowledgment

This work was supported by Taishan Scholar Construction Engineering by Shandong Government, National Natural Science Foundation of China (Grant Nos. 61403235, 61104050, 11201264, 61573221, 61633014), Natural Science Foundation of Shandong Province (Grant Nos. ZR2011AQ012, ZR2014FQ011).


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