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Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls

Author

Listed:
  • Yongxin Liu

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Hui Min

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

Abstract

In this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using switching controls . A verification theorem associated with a set of variational inequalities is established as a sufficient criterion for Nash equilibrium, in which the equilibrium switching strategies for the two players, indicating when and where it is optimal to switch, are characterized in terms of the so-called switching regions and continuation regions . The verification theorem is proved in a piecewise way along the sequence of total decision times of the two players. Then, some detailed explanations are also provided to illustrate the idea why the conditions are imposed in the verification theorem.

Suggested Citation

  • Yongxin Liu & Hui Min, 2024. "Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls," Mathematics, MDPI, vol. 12(24), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3976-:d:1546351
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    References listed on IDEAS

    as
    1. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    2. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    3. Sun, Jingrui & Yong, Jiongmin, 2019. "Linear–quadratic stochastic two-person nonzero-sum differential games: Open-loop and closed-loop Nash equilibria," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 381-418.
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