Funding may be available for the projects below, if there is no specific funding mentioned with the project details please check the 'Funding' tab for further options.

We also welcome applications from students who already have funding in place.

For further information contact the relevant supervisor.



Please note this list is not complete and applicants should contact staff members in whose research there are interested. 

Modelling, measurement and management of longevity and morbidity risk

  • Develop state of the art multi-population stochastic mortality models
  • Develop innovative new longevity risk management strategies
  • Investigate the underlying drivers of mortality
  • Develop new approaches to the modelling of morbidity for critical illness insurance

Scholarships are available on this research programme via the Actuarial Research Centre (ARC).


Enquiries should be emailed to Andrew Cairns. Further details can be found on the website.



Modelling cause-of-death mortality

Actuarial mortality studies have traditionally concentrated on all-causes mortality and have explored trends with respect to age and time. The need for better understanding of mortality improvement and enhanced awareness of factors affecting it, have led to widened interest in investigating mortality by cause of death. In this project we will consider stochastic models where the cause of death can be included as a potential driver for explaining trends in longevity and projecting future mortality rates.The project will also investigate how changes in causes of death (e.g. medical advances, socio-economic developments), and possibly their interactions, can influence mortality rates. Various statistical models will be considered under a Bayesian setting, aiming at characterising and quantifying the uncertainties associated with parameter estimation, available data and fitted model.

Supervisors: Dr G Streftaris and Dr T Kleinow


Approximating persistence times of endemic infections

The spread of infectious disease through a population may be modelled as a stochastic process. For infections which are able to persist in the long term (ie become endemic in the population), a random variable of interest is the time until eventual extinction of infection. For relatively simple models, the expected persistence time may be computed exactly from general Markov process theory. For more realistic models, this approach is no longer feasible, and approximations must be sought. This project will use recently-developed approximation methods from Hamiltonian statistical mechanics to investigate the effects of disease features (e.g. length of latent period, variability of infectious period, etc) upon persistence times.

Supervisor: Professor Damian Clancy


Novel Scaling Regimes for Networks: Theory and Applications

Understanding the interplay between different scaling frameworks is important in the application of queuing theory to many practical problems, for example the probability of loss of load in power networks and buffer overflow in telecommunication networks.  Traditionally a small range of scalings have been studied which often do not suit the practical applications; this project will explore novel scaling regimes and the probabilistic tools to study them. 

Supervisors: Dr James Cruise & Dr Fraser Daly


Optimal Coupling and Rates of Convergence to Stationarity for Markov Chains, with Applications

Consider two or more Markov chains on a finite state space, each starting from a different state but evolving using the same transition probability matrix.  This project will study how such Markov chains can be constructed (coupled) in an optimal way, for several different notions of optimality, and how knowledge about the time until the coalescence of trajectories may be applied in various settings.

Supervisors: Professor Sergey Foss & Dr Fraser Daly


Dynamic Properties of Multi-Dimensional Stochastic Processes, with Applications

We plan to develop probabilistic methods for studying long-time behaviour of complex stochastic processes with inter-dependent components.  Our results will have applications in wireless communication networks, queuing systems, energy, economics and other areas.

Supervisors: Professor Sergey Foss & Dr Seva Shneer


Model diagnostics for infectious epidemics


Stochastic modelling of communicable disease outbreaks is challenging due to inter-dependence in the involved transmission dynamics and imperfect observation of infection-related events. Estimation in such models is now well established, but research on model assessment and comparison is still under progress. This project will build on recently developed tools for epidemic model diagnostics to investigate the use of Bayesian methodology related to latent residuals, in cases where the epidemic outbreak is: (a) under-reported, (b) at early stages of its course, and (c) under the impact of intervention measures.

Supervisor: Dr George Streftaris


Numerical Methods for Financial Market Models

Many existing models for the evolution of financial and economic variables such as interest rates, inflation and so forth have no known closed-form solution.  In order to deal with such models, e.g. for pricing and risk management of financial derivatives, it is therefore of fundamental importance to design numerical methods that are highly accurate, fast and robust.  This project will apply methods from stochastic analysis and probability theory to models of financial markets to enhance the understanding of their stochastic properties, and to design high-quality fast methods for their numerical treatment.

Supervisors: Dr Anke WieseDr Simon Malham

Other projects may be available in the relevant areas which can be found on the Probability & Statistics Group website and the Actuarial & Financial Mathematics Group website. 

ARC scholarships

Several scholarships on 'Modelling, measurement and management of longevity and morbidity risk' are available via the Actuarial Research Centre, based at Heriot-Watt University. Find out more here.


MIGSAA studentship

EPSRC / SFC Centre for Doctoral Training: Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA) studentships. Find out more here.


EPSRC-funded PhD studentship

Applications are invited from eligible students for EPSRC-funded PhD studentship for up to 42 months to study any area of Applied Probability, Statistics, Actuarial Mathematics or Financial Mathematics. Candidates should have a strong mathematical background, including previous study of their chosen area.

British and Irish applicants are eligible for the full scholarship.  Other EU students are eligible for a fees only scholarship (i.e. no maintenance grant) and may be eligible for the full scholarship if they have completed their UG/PG studies in the UK in the past 3 or 4 years.

The full scholarship covers all tuition fees and an annual tax-free stipend which is currently around £14,000.

Information about research activities in the relevant areas can be found on the Probability & Statistics Group website and the Actuarial & Financial Mathematics Group website. 

Further enquiries should be addressed to Professor Damian Clancy.


James Watt scholarship

As part of an ambitious expansion programme to intensify further our world-leading research programmes, Heriot-Watt University is currently offering James Watt Scholarships in the School of Mathematical & Computer Sciences for the next academic year, opportunities may be available to both UK/EU and Overseas students.  For further details see here or contact Professor Damian Clancy.


MACS alumni scholarship

A 20% discount is available for all Heriot-Watt School of Mathematical and Computer Sciences graduates, with a 10% discount available for all other Heriot-Watt graduates. This discount will be applied automatically - there is no requirement to apply.

How to apply

Informal enquiries should be made to Professor Damian Clancy.

Full details of how to apply can be found here.

If applicable, please specify on the application form for which funding option you are applying.