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Lp-solutions of multi-dimensional BSDEs with mean reflection

Author

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  • Niu, Yue
  • Qu, Baoyou
  • Wang, Falei

Abstract

The present paper focuses on the investigation of multi-dimensional mean reflected backward stochastic differential equations (BSDEs) in a possibly non-convex reflection domain, whose generator also depends on the marginal probability distributions of the solution (Y,Z). Our main idea is to decompose the mean reflected BSDE into a BSDE and a deterministic Skorokhod problem. Then, utilizing Lp-estimates for BSDEs and Skorokhod problems, we explore the solvability of Lp-solutions (p>1) through fixed-point argument and an approximation approach under both inward normal and oblique reflection scenarios.

Suggested Citation

  • Niu, Yue & Qu, Baoyou & Wang, Falei, 2025. "Lp-solutions of multi-dimensional BSDEs with mean reflection," Stochastic Processes and their Applications, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:spapps:v:187:y:2025:i:c:s0304414925001048
    DOI: 10.1016/j.spa.2025.104663
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