The numerical solution of one-dimensional discrete asset pricing model based on the improved trigonometric extreme learning machine.

The asset pricing model plays an essential role in finance and has extended to all areas of finance and investment. This paper focuses on the numerical solutions of one-dimensional discrete asset pricing models, which can be translated into integral equations. To solve integral equations, an improved trigonometric extreme learning machine is developed, where the Fourier series is selected as the basis function. In particular, the sampling frequency of the trigonometric function varies with the property of data distribution, which helps to improve the accuracy of numerical solutions. The interior-point method is introduced to optimize the sampling frequency. Then, the integral equation is converted into a linear system which is solved by the extreme learning machine. This paper gives the mathematical derivation of solving the asset pricing model using the improved trigonometric extreme learning machine, which can be adapted to solve various types of integral equations. Subsequently, the improved trigonometric extreme learning machine is employed to solve the one-dimensional discrete-time asset pricing model. Simulation results demonstrate the high precision of the proposed method, which leads to less error in the approximate equity price and illustrates the feasibility of the improved trigonometric extreme learning machine. Furthermore, when the improved trigonometric extreme learning machine is compared with other related methods, the numerical simulations verify the efficiency and superiority of the proposed algorithm in solving the asset pricing model. • The IT-ELM is proposed to solve the discrete-time asset pricing model. • The sampling frequency is optimized by the interior-point algorithm. • The mathematical derivation of solving the asset pricing model is given. • The feasibility and the high precision of the IT-ELM are experimentally examined. [ABSTRACT FROM AUTHOR]