Mathematical Models in Finance and Industry (832G1)

15 credits, Level 7 (Masters)

Spring teaching

You will study partial differential equations arising in real-world problems related to both the industrial and the financial sector.

The module consists of two parts; in the first part you derive the advection-diffusion equation in one dimension, which models the transport of a pollutant in a flow, such as a river or column of air. You will begin with considering the advection and diffusion equations on the real line and on a bounded domain, and their solutions separately, and conclude with the full advection-diffusion equation. For each class of equation, where analytical solutions become difficult to obtain, you will consider schemes to approximate solutions.  

In the second part you will derive and solve the famous Black-Scholes equation for pricing of financial options. You will study this equation in the context of pricing European options and build up to the complex and interesting example of pricing of American options. In addition, you will develop central concepts of discrete and continuous time models of financial markets and analyse numerical methods for such problems, including their stability analysis. 


94%: Lecture
6%: Practical (Workshop)


100%: Written assessment (Report)

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2024/25. However, there may be changes to these modules in response to feedback, staff availability, student demand or updates to our curriculum. We’ll make sure to let you know of any material changes to modules at the earliest opportunity.


This module is offered on the following courses: