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Mean-Field and Anticipated BSDEs with Time-Delayed Generator

Author

Listed:
  • Pei Zhang

    (Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
    School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China)

  • Nur Anisah Mohamed

    (Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Adriana Irawati Nur Ibrahim

    (Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

In this paper, we discuss a new type of mean-field anticipated backward stochastic differential equation with a time-delayed generator (MF-DABSDEs) which extends the results of the anticipated backward stochastic differential equation to the case of mean-field limits, and in which the generator considers not only the present and future times but also the past time. By using the fixed point theorem, we shall demonstrate the existence and uniqueness of the solutions to these equations. Finally, we shall establish a comparison theorem for the solutions.

Suggested Citation

  • Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:888-:d:1063429
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    References listed on IDEAS

    as
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    4. Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.
    5. Qiang Han & Mehmet Emir Koksal, 2021. "Variable Step Size Adams Methods for BSDEs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, December.
    6. 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.
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