Postdoctoral scholarship (2 years) in Deep Learning for High-Dimensional Optimal Stopping and Stochastic Control

The Department of Mathematics and Mathematical Statistics at Umeå University is offering a postdoctoral scholarship within the project “Deep Learning for High-Dimensional Joint Optimal Stopping and Stochastic Control Problems with Applications in Finance”. 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
Many real-world decision-making problems involve both continuous control decisions and the choice of an optimal stopping time. Examples arise naturally in finance, forestry, agriculture, and aquaculture, where decisions about investment, treatment, feeding, or harvesting must be made under uncertainty. While optimal stopping and stochastic control problems have been studied extensively on their own, numerical methods for joint problems in high-dimensional settings remain a major scientific challenge.

The central aim of this project is to advance the understanding and solution of high-dimensional joint optimal stopping and stochastic control problems using modern mathematical and computational techniques. These problems are closely connected to Hamilton–Jacobi–Bellman variational inequalities (HJB-VIs), which provide a unifying theoretical framework but quickly become intractable with classical methods as the dimension increases.

The project offers three complementary scientific directions through which these challenges can be addressed:

1. PDE and analytical methods, focusing on the theory and properties of HJB variational inequalities combined with physics-informed neural networks (PINNs);
2. Deep Reinforcement Learning, where learning-based algorithms are used to approximate optimal policies and stopping strategies;
3. Forward–Backward (reflected) stochastic differential equation (F(R)BSDE) solvers, which provide probabilistic representations and numerical methods suitable for high-dimensional settings.

A key feature of the project is its flexibility: the precise focus and methodological approach will be adapted to the expertise, background, and scientific interests of the postdoctoral scholarship holder. The project is designed to allow the scholarship recipient to deepen existing strengths while developing new skills at the interface of (stochastic) analysis, numerical methods, and machine learning.

The postdoctoral researcher will have the opportunity to:

• pursue research along one or more of the three methodological directions described above,
• deepen their understanding of joint optimal stopping and stochastic control problems,
• apply developed methods to financially motivated and resource-management applications,
• collaborate with researchers within and beyond the department, such as AquaRisk (https://www.ntnu.edu/aquarisk/),
• disseminate results through publications and participation in international conferences and workshops.

This postdoctoral scholarship is financed and administered by the Kempe Foundation. 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 is required to 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, according to what is stipulated in the paragraph above, no later than three 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, 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:

• numerical methods for partial differential equations,
• (stochastic) optimal control and/or optimal stopping,
• machine learning or deep learning methods,
• scientific programming.

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 May 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:

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

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

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

We look forward to receiving your application!