May 2024 On Z-mean reflected BSDEs
Joffrey Derchu, Thibaut Mastrolia
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Bernoulli 30(2): 1502-1524 (May 2024). DOI: 10.3150/23-BEJ1642


In this paper we investigate the existence of (minimal) supersolutions to BSDEs with mean-reflection on the Z component. We first prove that classical methods to obtain conditions for the existence of supersolutions to BSDEs cannot be applied for this type of constraints. We show that, contrary to BSDEs with mean-reflections on the Y component, we cannot expect a supersolution with a deterministic increasing process K. Nonetheless, we give conditions for the existence of a supersolution for a stochastic component K and under various constraints. Finally, we turn to the existence of minimal supersolution by formalizing some previous arguments on the time-inconsistency of such problems. We formalize some previous arguments on the time-inconsistency of such problems, proving that a minimal supersolution is necessarily a solution in our framework. We apply the results to a replication problem with consumption-investment strategy under law constraints on the investment strategy. We show that the only strategy that might be optimal is the one with no investment.


The authors gratefully acknowledge the financial support of the ERC Grant 679836 Staqamof, the Chaires Analytics and Models for Regulation, and Financial Risk.


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Joffrey Derchu. Thibaut Mastrolia. "On Z-mean reflected BSDEs." Bernoulli 30 (2) 1502 - 1524, May 2024.


Received: 1 June 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699562
Digital Object Identifier: 10.3150/23-BEJ1642

Keywords: Constrained BSDEs , Malliavin calculus


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Vol.30 • No. 2 • May 2024
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