Some computational methods in finance

摘要

Partial Differential Equations (PDE) and Partial Integro-Differential Equations (PIDE) play a major role in financial mathematics and provide a powerful and consistent framework for pricing complex financial derivatives. However, since closed-form solutions are not available in general, numerical methods are often used. The article considers financial models based on exponential Levy processes, the PIDE derived from the models and different computational methods for solving these PIDE. A proposal for using Cellular Neural Networks (CNN) for solving PIDE is presented.