one PhD Scholarship for a project at the interface of Stochastic Analysis and Macro Economics

This PhD project develops a new quantitative framework for analysing how inequality and macroeconomic dynamics interact in modern economies. Classical overlapping generations (OLG) models are central to macroeconomics but typically treat shocks in a simplified way, focusing on aggregate disturbances while ignoring correlations across individuals and cohorts. Meanwhile, random growth models explain the fat-tailed distributions of income and wealth but abstract from intergenerational and macroeconomic feedbacks. This project unifies these perspectives by introducing random fields—stochastic processes indexed by both time and cohort—into continuous-time OLG models. Random fields enable both idiosyncratic (individual) and systematic (correlated) shocks to be modelled consistently, using stochastic partial differential equations (SPDEs) to describe how economic variables evolve and interact. This provides a richer, data-informed way to understand inequality and aggregate fluctuations. The research proceeds in four steps: (1) establishing the theoretical framework for random-field-driven OLG models; (2) applying Malliavin calculus and stochastic control to derive behavioural responses; (3) analysing stationary and transitional wealth distributions and the emergence of inequality “tails”; and (4) calibrating the model to UK data to evaluate the effects of taxation, pensions, and macroprudential regulation. By combining advanced quantitative methods with policy relevance, the project will advance understanding of how correlated shocks shape inequality and macroeconomic stability in the UK and beyond. It will also contribute to training a new generation of researchers fluent in the application of frontier stochastic methods to major social science challenges. Supervisory Team: First Supervisor: Professor Christian Ewald – christian.ewald@glasgow.ac.uk Second Supervisor: Professor Charles Nolan – charles.nolan@glasgow.ac.uk Third Supervisor: Dr Yihan Zou – yihan.zou@glasgow.ac.uk Eligibility Applicants must meet the following eligibility criteria: Applicants will have a degree (undergraduate) at 2:1 or above and have a demonstrable interest in the topic area under investigation. Applicants can have a Masters degree, however this is not a requirement. Applicants can study part-time or full-time