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2023 Generalized BSDE and reflected BSDE with random time horizon
Anna Aksamit, Libo Li, Marek Rutkowski
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Electron. J. Probab. 28: 1-41 (2023). DOI: 10.1214/23-EJP927


Motivated by structural, reduced-form and hybrid models of the third party and counterparty credit risk, we study a generalized backward stochastic differential equations (BSDE) up to a random time horizon ϑ, which is not a stopping time with respect to a reference filtration. In contrast to the existing literature in the area of credit risk modeling, we do not impose specific assumptions on the random time ϑ and we study the existence of solutions to BSDE and reflected BSDE with a random time horizon through the method of reduction. For this purpose, we also examine BSDE and reflected BSDE with a làdlàg driver where the driver is allowed to have a finite number of jumps overlapping with jumps of the martingale part. Theoretical results are illustrated by particular instances of a random time and explicit BSDEs in either the Brownian or Brownian-Poisson filtration.


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Anna Aksamit. Libo Li. Marek Rutkowski. "Generalized BSDE and reflected BSDE with random time horizon." Electron. J. Probab. 28 1 - 41, 2023.


Received: 14 July 2021; Accepted: 2 March 2023; Published: 2023
First available in Project Euclid: 9 March 2023

MathSciNet: MR4557762
zbMATH: 07707082
Digital Object Identifier: 10.1214/23-EJP927

Primary: 60G40 , 60H10 , 60H30 , 91G40

Keywords: BSDE , credit risk , Enlargement of filtration , random time , Reflected BSDE

Vol.28 • 2023
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