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General Mean-Field BDSDEs with Stochastic Linear Growth and Discontinuous Generator

Author

Listed:
  • Yufeng Shi

    (Institute for Financial Studies, Shandong University, Jinan 250100, China)

  • Jinghan Wang

    (Institute for Financial Studies, Shandong University, Jinan 250100, China)

Abstract

In this paper, we consider the general mean-field backward doubly stochastic differential equations (mean-field BDSDEs) whose generator f can be discontinuous in y . We prove the existence theorem of solutions under stochastic linear growth conditions and also obtain the related comparison theorem. Naturally, we present those results under the linear growth condition, which is a special case of the stochastic condition. Finally, a financial claim sale problem is discussed, which demonstrates the application of the general mean-field BDSDEs in finance.

Suggested Citation

  • Yufeng Shi & Jinghan Wang, 2024. "General Mean-Field BDSDEs with Stochastic Linear Growth and Discontinuous Generator," Mathematics, MDPI, vol. 12(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:978-:d:1363572
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    References listed on IDEAS

    as
    1. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    2. Owo, Jean-Marc, 2015. "Backward doubly stochastic differential equations with stochastic Lipschitz condition," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 75-84.
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