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Stochastic Optimal Control Problem in Advertising Model with Delay

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Abstract

This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.

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Authors and Affiliations

  1. School of Science, China University of Mining & Technology, Beijing, 100083, China

    Li Chen

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    Zhen Wu

Authors
  1. Li Chen
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  2. Zhen Wu
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Corresponding author

Correspondence to Zhen Wu.

Additional information

This research was supported by the Natural Science Foundation of China under Grant Nos. 11301530, 11831010, 61961160732, 61977043, and the Natural Science Foundation of Shandong Province under Grant Nos. ZR2017MA049 and ZR2019ZD42.

This paper was recommended for publication by Editor SUN Jian.

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Chen, L., Wu, Z. Stochastic Optimal Control Problem in Advertising Model with Delay. J Syst Sci Complex 33, 968–987 (2020). https://doi.org/10.1007/s11424-020-8185-1

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  • DOI: https://doi.org/10.1007/s11424-020-8185-1

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