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A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations

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  • Jie Xu

    (Henan Normal University)

  • Qiqi Lian

    (Henan Normal University)

Abstract

In this paper, we study the strong convergence rate of the averaging principle of two-time-scale forward-backward stochastic differential equations (FBSDEs, for short). First, we present the well-posedness of the objective equations and then we give some a priori estimates for FBSDEs, backward stochastic auxiliary equations and backward stochastic averaged equations. Second, a strong convergence rate of the averaging principle for two-time-scale FBSDEs is derived. As far as we know, this is the first result on the strong convergence rate of the averaging principle of two-time-scale backward stochastic differential equations (BSDEs, for short).

Suggested Citation

  • Jie Xu & Qiqi Lian, 2023. "A Strong Convergence Rate of the Averaging Principle for Two-Time-Scale Forward-Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2590-2610, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01278-1
    DOI: 10.1007/s10959-023-01278-1
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    References listed on IDEAS

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    1. Dmitry Kramkov & Sergio Pulido, 2014. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Papers 1410.6144, arXiv.org, revised Aug 2016.
    2. Bahlali, Khaled & Elouaflin, Abouo & Pardoux, Etienne, 2017. "Averaging for BSDEs with null recurrent fast component. Application to homogenization in a non periodic media," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1321-1353.
    3. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    4. Dmitry Kramkov & Sergio Pulido, 2016. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Post-Print hal-01181147, HAL.
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