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Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks
Methodology and Computing in Applied Probability ( IF 0.9 ) Pub Date : 2022-03-15 , DOI: 10.1007/s11009-022-09946-1
Maximilien Germain , Joseph Mikael , Xavier Warin

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations (FBSDEs). Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean-field games and mean-field control problems in moderate dimension. We analyze the numerical behavior of our algorithms on several multidimensional examples including non linear quadratic models.



中文翻译:

使用神经网络的 McKean-Vlasov FBSDE 的数值分辨率

我们提出了几种算法来求解 McKean-Vlasov 前向后向随机微分方程 (FBSDE)。我们的方案依靠神经网络的逼近能力通过最小化问题来估计解或其梯度。因此,我们获得了能够在中等维度上解决平均场博弈和平均场控制问题的方法。我们在包括非线性二次模型在内的几个多维示例上分析了我们的算法的数值行为。

更新日期:2022-03-15
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