Postdoctoral scholarship (2 years) in Stochastic Overlapping Generations Models, Random Fields, and Inequality Dynamics

The Department of Mathematics and Mathematical Statistics at Umeå University is offering a postdoctoral scholarship within the project “Random Fields in Continuous-Time Overlapping Generations Models: Wealth Inequality and Macroeconomic Dynamics ”. The scholarship is full-time for two years, with a starting date of 1 September 2026 or by agreement.

The Department of Mathematics and Mathematical Statistics conducts research in applied and theoretical mathematics, including computational methods and financial mathematics. The successful candidate will be associated with a growing research environment in applied stochastic control, deep learning, and quantitative finance, and will have opportunities for collaboration within the department as well as with national and international partners.

Project description
Understanding wealth and income inequality is one of the central challenges in modern economics. While continuous-time overlapping generations (OLG) models provide a tractable framework for intergenerational macroeconomic analysis, and random growth models explain fat-tailed wealth distributions, these strands of research have not yet been fully integrated.

The objective of this project is to develop a unified continuous-time stochastic OLG framework in which both idiosyncratic and systematic shocks are modeled as random fields. The project introduces stochastic partial differential equations (SPDEs) and Malliavin calculus into macroeconomic modeling to analyze:

• intergenerational wealth accumulation,
• correlated aggregate and idiosyncratic shocks,
• tail behavior of wealth distributions,
• transition dynamics of inequality,
• and policy effects (taxation, pensions, financial stability).

The project connects stochastic analysis, infinite-dimensional control theory, and macroeconomic inequality theory, including operator methods inspired by the inequality dynamics literature.

The postdoctoral researcher will  have the opportunity to build merits in several interconnected areas:

1. Random Fields and SPDEs in OLG Models
Formulation of wealth, income, and mortality processes as random fields indexed by time and cohort (or space), with dynamics governed by SPDEs driven by time–space Brownian motion.

2. Malliavin Calculus and Stochastic Maximum Principles
Development of Malliavin-based stochastic maximum principles for SPDE-driven OLG systems, extending martingale methods to infinite-dimensional settings.

3. Inequality Dynamics and Tail Behavior
Characterization of stationary and transient wealth distributions, tail exponents, and transition speeds under correlated shocks.

4. Policy Analysis
Evaluation of taxation, pension systems, and macro-prudential regulation in stochastic environments with systematic and idiosyncratic risk.

The precise emphasis will be adapted to the background and strengths of the postdoctoral scholar. The project allows specialization in:

• stochastic analysis and SPDE theory,
• Malliavin calculus,
• infinite-dimensional stochastic control,
• macroeconomic modeling of inequality,
• or numerical SPDE simulation and calibration.

This postdoctoral scholarship is financed and administered by Kempestiftelserna. The stipend is tax-free and will be 750 000 SEK for two years, meaning 375 000 SEK per year.

Qualifications
To qualify as a postdoctoral scholarship holder, the postdoctoral fellow must have completed a doctoral degree or a foreign degree deemed equivalent to a doctoral degree. This qualification requirement must be fulfilled no later than the time of the decision about the scholarship recipient.

Priority should be given to candidates who completed their doctoral degree, as stipulated in the paragraph above, no later than 3 years prior. If there are special reasons, candidates who completed their doctoral degree prior to that may also be eligible. Special reasons include absence due to illness, parental leave, appointments of trust in trade union organizations, military service, or similar circumstances, as well as clinical practice or other forms of appointment/assignment relevant to the subject area.

A doctoral degree in mathematics, applied mathematics, mathematical finance, quantitative economics, or a related discipline is required. Good knowledge of written and spoken English is required.

Meritorious qualifications include documented experience or a strong interest in one or more of the following areas:

• Stochastic partial differential equations (SPDEs)
• Malliavin calculus
• Infinite-dimensional stochastic control
• Continuous-time macroeconomic modeling
• Inequality dynamics and wealth distribution theory
• Spectral/operator methods
• Scientific computing and Monte Carlo simulation

Application
A full application should include:

• a cover letter (maximum 2 pages excluding references) describing your research interests, motivation for applying, and how your previous experience relates to the project,
• curriculum vitae (CV), including a publication list,
• a verified copy of the doctoral degree certificate or documentation clarifying when the doctoral degree is expected to be obtained,
• verified copies of other diplomas, lists of completed academic courses, and grades,
• a copy of the doctoral thesis (or, if not yet available, a summary of the thesis, maximum 5 pages),
• any additional documents the applicant wishes to submit,
• Contact information for two persons willing to act as references.

The application should be written in English (preferably) or Swedish, and the attached documents should be in Word or PDF format. The application should be registered via Umeå University’s e-recruitment system Varbi and submitted no later than 31 March 2026.

Umeå University strives to offer an equal environment where open dialogue between people with different backgrounds and perspectives lies the foundation for learning, creativity, and development. We welcome people with different backgrounds and experiences to apply for this scholarship, and especially encourage female applicants.

More information
Further details are provided by:

Christian Ewald, Professor
Department of Mathematics and Mathematical Statistics, Umeå University
E-mail: christian.ewald@umu.se

Kevin Kamm, Associate Professor
Department of Mathematics and Mathematical Statistics, Umeå University
E-mail: kevin.kamm@umu.se

More information about the department: https://www.umu.se/en/department-of-mathematics-and-mathematical-statistics/