The application of improved physics-informed neural network (IPINN) method in finance.

With the development of computers and neural networks, the traditional methods of solving differential equations have been greatly developed. Typical examples are the differential equations of population, finance, infectious disease and traffic problems solved by neural network method. Recently, the popular physics-informed neural network (PINN) method has been proved to be able to solve the numerical solution of PDEs. Based on the PINN method, this paper proposes an improved PINN method (IPINN) that is to introduce local adaptive activation function of neurons into PINN network to improve the performance of neural network and successfully applies the IPINN method to the Ivancevic option pricing model and Black–Scholes model in finance. The rogue wave solution and soliton solution of the Ivancevic option pricing model, and the numerical solution of the Black–Scholes model are solved, respectively. At the same time, it can be shown that the IPINN method has the characteristics of faster convergence, more stability and higher accuracy than the PINN method by the results of numerical experiments. [ABSTRACT FROM AUTHOR]