论文标题
二次平均场反射BSDE
Quadratic Mean-Field Reflected BSDEs
论文作者
论文摘要
在本文中，当驾驶员在第二个未知$ z $中具有二次增长时，我们分析了平均场反射的随机微分方程。使用线性化技术和BMO Martingale理论，我们首先应用固定点论点来确立具有有限的终端条件和障碍的情况的唯一性和存在结果。然后，借助$θ$ -METHOD，我们开发了一个连续的近似过程，以删除终端条件上的有界条件，当发电机相对于第二个未知$ z $时，发电机是凹入（或凸）时
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 $θ$-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 $z$
