Asset pricing model is the pillar of modern financial market price theory. It is of great practical and theoretical significance to solve the equilibrium price-dividend function of the asset pricing model. To solve the asset pricing model, this paper develops a novel neural network method called improved trigonometric neural network, which consists of three parts: the improved trigonometric function, the initial-condition extreme learning machine algorithm and the reduction algorithm. First, the equilibrium price-dividend function is described as a stochastic differential equation and this function is translated into a second-order ordinary differential equation equivalently. Second, the improved trigonometric neural network is used to solve the differential equation with initial conditions, where the improved trigonometric function is used to serve as the activation function. The reduction algorithm is proposed to obtain a simpler network structure and a faster computing speed. Third, numerical experiments of the improved trigonometric neural network show that the numerical solution of the price-dividend function will be obtained precisely, quickly and feasibly. Compared with several methods to solve asset pricing model, the improved trigonometric neural network has the highest accuracy and fastest speed.

资产定价模型是现代金融市场价格理论的基础。解决资产定价模型的均衡价格分红函数具有重要的实践和理论意义。为了解决资产定价模型，本文开发了一种新的神经网络方法，称为改进三角神经网络，它由三个部分组成：改进的三角函数，初始条件极限学习机算法和归约算法。首先，将均衡价格分红函数描述为随机微分方程，然后将该函数等效转换为二阶常微分方程。其次，使用改进的三角神经网络求解具有初始条件的微分方程，其中改进的三角函数用作激活函数。提出了约简算法以获得更简单的网络结构和更快的计算速度。第三，改进的三角神经网络的数值实验表明，可以精确，快速，可行地获得价格分红函数的数值解。与几种求解资产定价模型的方法相比，改进的三角神经网络具有最高的准确性和最快的速度。