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Time-delayed generalized BSDEs

Author

Listed:
  • Di Persio, Luca
  • Garbelli, Matteo
  • Maticiuc, Lucian
  • Zălinescu, Adrian

Abstract

We prove the existence and uniqueness of the solution of a BSDE with time-delayed generators in the small delay setting (or equivalently small Lipschitz constant), which employs the Stieltjes integral with respect to an increasing continuous stochastic process. Moreover, we obtain a result of continuity of the solution with regard to the increasing process, assuming only uniform convergence, but not in variation. We also prove the existence in the case of arbitrary delay by imposing monotonicity and linearity on generators. Lastly, we provide an application of the theoretical framework within an insurance based example.

Suggested Citation

  • Di Persio, Luca & Garbelli, Matteo & Maticiuc, Lucian & Zălinescu, Adrian, 2024. "Time-delayed generalized BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:spapps:v:170:y:2024:i:c:s0304414923002491
    DOI: 10.1016/j.spa.2023.104277
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