Time-delayed generalized BSDEs

Luca Di Persio, Matteo Garbelli, Lucian Maticiuc and Adrian Zălinescu

Stochastic Processes and their Applications, 2024, vol. 170, issue C

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.

Keywords: Generalized backward stochastic differential equations; Time–delayed generators; Stieltjes integral; Parameter dependence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104277

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