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Quadratic mean-field reflected BSDEs

Ying Hu’s research is supported by the Lebesgue Center of Mathematics “Investissements d’avenir” Program (Grant No. ANR-11-LABX-0020-01), by ANR CAESARS (Grant No. ANR-15-CE05-0024) and by ANR MFG (Grant No. ANR-16-CE40-0015-01). Falei Wang’s research is supported by the Natural Science Foundation of Shandong Province for Excellent Youth Scholars (Grant No. ZR2021YQ01), the National Natural Science Foundation of China (Grant Nos. 12171280, 12031009 and 11871458), and the Young Scholars Program of Shandong University.

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  • In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown $ z $. Using a linearization technique and the BMO martingale theory, we first apply a fixed-point argument to establish the uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of the $ \theta $ -method, we develop a successive approximation procedure to remove the boundedness condition on the terminal condition and obstacle when the generator is concave (or convex) with respect to the second unknown $ z $.

    Mathematics Subject Classification: 60H10, 60H30.

    Citation:

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