Solving financial differential equations with neural networks

Overview

Partial differential equations are a category of complex mathematical problems that can represent a vast range of systems, often lacking exact solutions. Approximate solutions can be found using numerical methods, which involve iterative calculations and can be quite time-consuming.

Problem

A client working in the financial sector reached out to request the development of an algorithm for solving partial differential equations, regarding the pricing of financial options, which have no analytical solution.

Solution

To tackle this challenge I developed an algorithm based on highway neural networks. This algorithm is used for the solution of partial differential equations, and is found in the scientific literature. This work involved adapting the mathematical framework to meet the specific client's needs.