# Choosing my dissertation topic

Mohammad Tahir discusses how he chose a research topic for his dissertation, the process of working on it and how it has helped with his future

“When I was asked to choose a research topic for my dissertation, I was unclear what I wanted to write my dissertation about. The only thing I knew is that I wanted my dissertation to relate to finance. After researching the use of mathematics in finance and talking to some of my lecturers, I decided to write my dissertation on the cardinality-constrained mean-variance portfolio optimisation problem. This problem interested me because it is one of the most important problems to solve in order for an investor to manage their portfolios efficiently.”

I started working on my dissertation in the summer, just before my final year at Plymouth. Initially, I found the research process challenging as I was unsure where to start. I started to read a book called Modern Portfolio Theory and Investment Analysis written by Edwin J. Elton. This book was beneficial and gave me a good idea of where I wanted to start. I continued working on relatively easy topics to understand and then moved on gradually to explore the problematic part of my research area.

The mean-variance portfolio optimisation problem asks: given a universe of assets (stocks, shares, commodities) and a limited budget, how can we choose the optimal proportions for each asset as part of a portfolio? The standard objectives are that expected portfolio return has to be maximised, while portfolio risk is minimised. The cardinality-constrained version of the problem confines the investor to a certain subset (typically 5 or 10) of assets, where the same objectives must be achieved. This problem is complex, in fact NP-hard – it cannot be solved numerically and in practice metaheuristic optimisation methods such as genetic algorithms and particle swarm optimisers are used to give approximate (but very accurate) solutions to the problem. I took my existing knowledge of the programming language R I learnt earlier in my degree and, improving that knowledge, I implemented a metaheuristic approach.

During my research, I wasn’t sure what issues I should focus on first and I was trying to explore different topics at the same time. From my experience, this is not an ideal approach and I wouldn’t recommend it. My supervisor, Dr Mathew Craven, was very helpful and helped me to restrict my focus to explore one topic at a time.

The most challenging stage of the project was writing the metaheuristic in the form of a code in R and analysing the obtained results. Dr Craven was incredibly helpful at this stage of my research in providing resources such as research papers and helped me to understand the concepts that were difficult to grasp.

Working on my dissertation and using my computer for long hours during the Coronavirus lockdown was stressful. However, I believe I had more time to work on my study, particularly my dissertation, than I would have had in normal circumstances. Working on this project has helped me in my future career, and I will begin an MSc in Economics this September.

My tip for anyone planning to do their dissertation is to start collecting as much information as you can about the problem by doing a lot of reading. Most importantly, don’t panic and make the most of your supervisor’s knowledge.

MATH3628 Mathematics Final Year Project

This 40-credit module allows students to spend a substantial amount of time studying a topic of their own interest under the direction of an expert member of staff. This topic could be anything you choose in Theoretical Physics, Applied Mathematics, Pure Mathematics or Statistics. Examples of projects include Offshore Renewable Energy, Cryptography, Gravitational Lensing and many more besides.