论文标题
BSDE的离散化和机器学习近似，并限制了收益过程
Discretization and Machine Learning Approximation of BSDEs with a Constraint on the Gains-Process
论文作者
论文摘要
我们研究了向后的随机微分方程（简称BSDE）的近似值，对增益过程有限制。我们首先通过在网格时应用所谓的改头换面操作员来离散约束。我们表明，随着网格网格收敛到零，这种离散限制的BSDE会收敛到连续约束的BSDE。然后，我们专注于离散约束BSDE的近似值。为此，我们采用机器学习方法。我们表明，在神经网络及其衍生物的约束下，对一类神经网络的优化问题可以近似。然后，随着神经元的数量流入无穷大，我们得出了一种收敛到离散约束BSDE的算法。我们以数值实验结束。数学主题分类（2010年）：65C30，65M75，60H35，93E20，49L25。
We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments. Mathematics Subject Classification (2010): 65C30, 65M75, 60H35, 93E20, 49L25.
