Abstract
We consider the deep learning based scheme proposed in [W. E and J. Han and A. Jentzen, Commun. Math. Stat., 5 (2017), pp. 349–380] and study the effect of the number of neural networks on the gradient of the solution. We demonstrate that using one neural network improves its numerical stability for the whole path and also reduces the computational time. This is illustrated with several 100-dimensional nonlinear backward stochastic differential equations including nonlinear pricing problems in finance.
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Kapllani, L. (2022). The Effect of the Number of Neural Networks on Deep Learning Schemes for Solving High Dimensional Nonlinear Backward Stochastic Differential Equations. In: Ehrhardt, M., Günther, M. (eds) Progress in Industrial Mathematics at ECMI 2021. ECMI 2021. Mathematics in Industry(), vol 39. Springer, Cham. https://doi.org/10.1007/978-3-031-11818-0_10
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