Quadratic BSDEs with mean reflection

2017/05/27 by Hélène Hibon, Hibon, Hélène, Ying Hu +7 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1705.09852

openalex publication_date 2017/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the z argument. This work is the sequel of Briand et al. [BSDEs with mean reflection, arXiv:1605.06301] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the y argument.

Citations

• Utility maximization in incomplete markets

Cited by

• Backward Stochastic Differential Equations with Nonlinear Expectation Reflection
• Mean-field BSDEs with non-Lipschitz coefficients and double mean reflections

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