Quadratic Mean-Field Reflected BSDEs

Ying Hu; Remi Moreau; Falei Wang

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arXiv · 2201.10359

Quadratic Mean-Field Reflected BSDEs

Ying Hu·Remi Moreau·Falei Wang

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Abstract

In this paper, we analyze mean-field reflected backward stochastic differential equations when the driver has quadratic growth in the second unknown $z$. Using linearization technique and BMO martingale theory, we first apply fixed point argument to establish uniqueness and existence result for the case with bounded terminal condition and obstacle. Then, with the help of a $\theta$-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 2nd unknown $z$

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Ying Hu, Remi Moreau, Falei Wang. 2022-01-25. Quadratic Mean-Field Reflected BSDEs. https://arxiv.org/abs/2201.10359

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