A novel improved trigonometric neural network algorithm for solving price-dividend functions of continuous time one-dimensional asset-pricing models.

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. [ABSTRACT FROM AUTHOR]