PhD Position Numerical Methods for Stochastic Differential Equations

Job description

The Analysis research group within the Delft Institute of Applied Mathematics at TU Delft is offering a full-time PhD position in the area of Numerical Methods for Stochastic Differential Equations. The PhD candidate will be supervised by Dr. Kristin Kirchner (TU Delft and KTH Royal Institute of Technology Stockholm).

The focus of the project lies on the numerical approximation of solutions to stochastic differential equations, which due to the form of these equations are not Markov processes. Such stochastic processes "with memory" are of importance in several disciplines, such as for financial and statistical modelling. However, due to the correlation structure their computational simulation is very challenging. The PhD project addresses this challenge. Possible topics are computational methods for stochastic equations driven by fractional Brownian motion and multilevel Monte Carlo methods. Applications include option pricing under rough volatility models in finance and long-range dependencies in statistics.

The project includes the budget for a research visit at KTH Royal Institute of Technology in Stockholm, Sweden.

Besides carrying out mathematical research and working on scientific articles, the PhD candidate is expected to actively participate in seminars and discussions with colleagues from the department as well as to present the findings at (inter)national conferences or workshops. Furthermore, the candidate is supposed to carry out minor teaching tasks (at most 15% of the contract time). Teaching in English will be possible. Communication will be in English.

The project is for a duration of 4 years.

The starting date has to be on or before 15 September 2024.

Requirements

Your profile:

• Completed Master's degree or diploma in the field of Mathematics or a closely related field (completed or about to be completed).
• A strong background in Numerical Analysis and/or in Probability Theory.
• Enthusiasm for abstract mathematical problems and persistance in solving them.
• Capability of working both independently and collaboratively in a team.
• Programming skills (Matlab and/or Python).
• Excellent proficiency in written and spoken English.

Doing a PhD at TU Delft requires English proficiency at a certain level to ensure that the candidate is able to communicate and interact well, participate in English-taught Doctoral Education courses, and write scientific articles and a final thesis.

Conditions of employment

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2770 per month in the first year to € 3539 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance, and a monthly work costs contribution. Flexible work schedules can be arranged.

For international applicants, TU Delft has the Coming to Delft Service. This service provides information for new international employees to help you prepare the relocation and to settle in the Netherlands. The Coming to Delft Service offers a Dual Career Programme for partners and they organise events to expand your (social) network.

TU Delft (Delft University of Technology)

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

Faculty Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future-proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment – which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground-breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4,000 students work and study in this innovative environment.