Dynamical Behavior and Calculation of Solution for European Option Pricing Model with Transaction Costs and Dividend Payments

Based on the traditional Black–Scholes option pricing model, we consider a European option pricing model with transaction costs and dividend payments. In our paper, we use the Galerkin method to study the existence of a solution of this model. Meanwhile, by using the energy estimation method, we also study the exponential stability of the solution to this model. Moreover, an approximate solution is obtained by the Fourier method for a simplified case of this model. Lastly, the approximate solution is illustrated by numerical experiments.