PhD position in Financial maths

The Department of Mathematics at the University of Manchester invites applications for a PhD position in Financial Mathematics and Actuarial Science. The application deadline is 15th January 2027. The successful candidate will work with Dr Thomas Bernhardt on the project 'Tontines: diverse cohorts and automated adjustments'. Description of the project: The project is about future pension funds, called tontines. Those are the subject of current government consultations (under the name decumulation-only CDC schemes). In such funds, retirees' income is adjusted based on experienced mortality rates of other retirees in the same scheme. Predicting and controlling the fluctuation is crucial. The project aims to analyse income fluctuations when retirees are of different ages (different mortality distributions), and initial assumptions are wrong (the actual mortality distribution differs from the assumed one). Mathematically, finding a description that allows for limiting arguments is a challenge. Based on previous work, I expect the project to work on mixtures of deterministically time-changed Brownian motions. To answer questions relevant to tontines, the project will adjust (and develop new) functional limiting theorems from probability theory, such as Berry-Esseen bounds, which in their current form fail to produce numerically observed phenomena. In previous work, assuming a fixed mortality distribution but heterogeneous wealth has led to new optimisation problems involving finding an optimal histogram in a constrained optimisation problem for distributions. The PhD 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. Important details: -The project is expected to start in September 2027. -The deadline to apply for the first round is 1st November 2026, and for the second round 15th January 2027. -Funding is available but competitive (covering tuition fees and a stipend of currently £21,805 per year for 3.5 years). -For more details and how to apply, see the links below: https://www.findaphd.com/phds/project/school-of-natural-sciences-phd-scholarships-tontines-diverse-cohorts-and-automated-adjustments/?p198776 https://pgapplication.manchester.ac.uk/psc/apply/EMPLOYEE/SA/c/CIBAA_MNU.UMOAA_LOGIN_CMP.GBL?Page=CIBAA_LOGIN&Action=A