Self-funded PhD opportunities

Construction of moment-based goal programming models for sustainable portfolio selection

  • Application end date: Saturday 1 July 2017
  • Funding Availability: Self-funded PhD students only
  • Department: Mathematics
  • PhD Supervisor: Khian Sim and Dylan Jones

This project will develop a new class of mathematical portfolio selection models that allow the selection of portfolios in accord with investors’ preferences by consideration and combination of two additional data sources. The first source is the higher moments of the asset and portfolio return statistical distributions. The project will go beyond the consideration of the third (skewness) and fourth (kurtosis) moments to produce generic moment-based portfolio selection models that can be formulated as high-order polynomial and semi-infinite goal programmes. These will then be solved using mathematical programming modelling software. The second factor is the inclusion of sustainability (economic, environmental and social) factors in order to produce portfolio that is tailored to the individual investor’s preferences and beliefs. An analysis of the sustainability factors of a set of assets will be undertaken and hence sustainability factors will be incorporated into the goal programming portfolio selection models. Sensitivity analysis of the results will be undertaken and conclusions drawn.

This opportunity will suit a candidate with a degree level or masters qualification in mathematics, statistics, operational research or finance who is looking to further their career in the operational research or analytics field. Candidates should be enthusiastic about the topic and willing to work with academic and research staff within the Centre for Operational Research and Logistics (CORL) ( The ideal candidate would also have some experience of modelling and solving mathematical, statistical or operational research models by computerised software. The successful candidate will work alongside the supervisory team of Dr Chee-Khian Sim and Prof Dylan Jones, as well as participating in regular research events from CORL and the Department of Mathematics. PhD candidates in the operational research domain have traditionally been given the opportunity to participate in multiple NATCOR ( courses as part of their research training.

How to apply

To apply or make an enquiry, please visit postgraduate research: Mathematics and Physics

Applications should use our standard application forms and follow the instructions given under the ‘Research Degrees’ heading on the following webpage:

When applying please note the project code: MPHY3340217

Funding Notes: Home/EU applicants only. Please use the online application form and state the project code and studentship title in the personal statement section.

An appropriate first or upper second class honours degree of any United Kingdom university or a recognised equivalent non-UK degree of the same standard honours degree or equivalent in a relevant subject or a master’s degree in an appropriate subject. Exceptionally, equivalent professional experience and/or qualifications will be considered.

References to recent published articles:

1. Hu, Y., Yang, X. & Sim CK (2015) Inexact subgradient methods for quasi-convex optimization problems, European Journal of Operational Research, 240, 315-327.

2. Jones DF and Tamiz M (2010) Practical Goal Programming, Springer. New York.

3. Jones DF (2011) A practical weight sensitivity algorithm for goal and multiple objective programming, European Journal of Operational Research, 213, 238-245.