About the Project
The world faces an ongoing retirement crisis. Governments and insurance companies seek retirement products that cope with rising life expectancy and uncertain financial markets. In the UK, tontines have gained attention as potential solutions. They deal with an uncertain future by adjusting retirees' income over time. In particular, tontines remove costly guarantees, but their members bear the risk of an uncertain future income. They are currently being discussed in ongoing government…
consultations.
Tontines are sustainable alternatives to guaranteed pensions. But a fluctuating income is a problem for pensioners. Predicting and controlling the fluctuation is crucial. However, making long-term predictions about income payments decades in advance is a challenge. Specification errors have a cumulative effect on the income payments.
We aim to understand how different age cohorts affect the income fluctuations. In particular, we want to decide whether each member benefits from being together in the tontine. The project builds on previous ground-breaking research on the case of one cohort with a fixed mortality distribution. Here, probabilistic limit theorems and stochastic analysis have yielded precise predictions decades in the future without using simulations.
We aim to adapt the income optimally when we assume one mortality distribution but face a different one. We might initially use a national life table but deviate from it over time. For example, regulation prohibits treating individuals differently based on protected characteristics like sex. However, females tend to have a different mortality distribution than males. We study how tontines can function well regardless of the male-to-female ratio in their membership.
In this project, the PhD candidate will learn about the current developments on tontines. The candidate will develop and use appropriate functional limit theorems from probability theory suitable for stochastic processes appearing in the context of tontines. The candidate is expected to produce results similar in nature and quality to those in the following paper: Wealth heterogeneity in a closed pooled annuity fund by Thomas Bernhardt & Ge Qu (2024), DOI: 10.1080/03461238.2023.2234916.
This project is expected to start in September 2027.
Before you apply: We strongly recommend that you contact the supervisors for this project before you apply.
How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships. If you don't already have an applicant account, please follow the instructions here.
When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications. Please note late or incomplete applications will not be considered.
Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status.
We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder.
Eligibility: The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Mathematics OR any upper-second class (2:1) honours degree and a Master's degree at merit (or international equivalent) in Mathematics. Previous research experience or knowledge of probability theory and functional limit theorems is essential.
This project will remain open until filled.
If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026.
If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027.
Self or externally funded students can also be considered for this project.
FSE_SoNS
Funding Notes
Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.