We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio. In numerical experiments, the new decision function significantly improves the original model of Hutchinson-Lo-Poggio with faster convergence and better generalization performance. By proving a novel universal approximation theorem, we show that our decision function rather than Hutchinson-Lo-Poggio's can be approximated on the entire domain of definition by neural networks. Thus the experimental results are partially explained by the representation properties of networks.

翻译：我们提出了一个时间价值相关决定功能,用于处理Hutchinson-Lo-Poggio提出的典型选择定价问题。在数字实验中,新的决定功能大大改进了Hutchinson-Lo-Poggio的原始模型,加快了趋同速度,提高了一般化性能。 通过证明一个新的通用近似理论,我们证明我们的决定功能,而不是Hutchinson-Lo-Poggio的功能,可以通过神经网络在整个定义领域进行近似。因此,实验结果部分地由网络的代表性特性来解释。