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Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations

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Abstract

A kind of linear-quadratic Stackelberg games with the multilevel hierarchy driven by both Brownian motion and Poisson processes is considered. The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations (FBSDEs) with Poisson processes (FBSDEPs) in a closed form. By the continuity method, the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871310, 11801317, 61873325 and 11831010), the Natural Science Foundation of Shandong Province (Grant No. ZR2019MA013), the National Key R&D Program of China (Grant No. 2018YFA0703900), and the Colleges and Universities Youth Innovation Technology Program of Shandong Province (Grant No. 2019KJI011).

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Authors and Affiliations

  1. School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China

    Na Li

  2. Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China

    Jie Xiong

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

    Zhiyong Yu

Authors
  1. Na Li
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  2. Jie Xiong
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  3. Zhiyong Yu
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Correspondence to Zhiyong Yu.

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Li, N., Xiong, J. & Yu, Z. Linear-quadratic generalized Stackelberg games with jump-diffusion processes and related forward-backward stochastic differential equations. Sci. China Math. 64, 2091–2116 (2021). https://doi.org/10.1007/s11425-019-1677-5

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  • DOI: https://doi.org/10.1007/s11425-019-1677-5

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