Subject areas:
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Funding type:
Research Training & Support Grant.
Stipend.
Tuition fee.
Fully-funded PhD studentship available to start in the 2025/26 academic year.
Award details
The project will focus on pathwise methods in stochastic analysis and broadly its application in mathematical finance. Traditionally, Itô's lemma provides a change-of-variable formula for semimartingales, interpreting the stochastic integral as the limit of left Riemann sums which exist in a well-defined probabilistic sense. However, this framework is limited to semimartingales and does not extend to more irregular processes or processes which are not Gaussian.
To address this, Hans Föllmer introduced a pathwise approach by considering càdlàg paths with finite quadratic variation along a sequence of partitions. This framework allows for the definition of stochastic integrals as pointwise limits of left Riemann sums along a partition sequence, making it possible to extend stochastic calculus beyond the semimartingale setting. Recent advancements have further explored the existence of stochastic integrals in contexts involving rougher paths than semimartingales.
This PhD project will focus on:
- Developing pathwise methods for measuring the roughness index of stochastic processes.
- Investigating rough-Itô isometry and the invariance properties of stochastic integrals.
- Exploring applications of these concepts in financial mathematics, particularly in model-free finance.
Candidates will have the opportunity to contribute to the theoretical foundations of pathwise stochastic calculus and its practical applications in finance.
Award value
The studenrship covers the following:
- Stipend
- Bench Fees
- Tuition fees (full Home or Overseas tuition fees)
- Funding is available for 3.5 years
Eligibility criteria
Award open to UK and international students.
Applicants should have a 2:1 or first-class undergraduate degree, or an MMath, MSci or Master’s degree with Merit and high grades in modules relating to the research area.
Application process
To be considered for the position, candidates must apply via King’s Apply online application system. Details are available at following website.
Please apply for “Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability MPhil/PhD”, indicate Dr. Purba Das as the supervisor and quote the project title in your application and all correspondence.
Please ensure to add the following code StartUpDas
in the Funding section of the application form. Please select option 5: ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly.
The selection process will involve a pre-selection on documents and, if selected, will be followed by an invitation to an interview. If successful at the interview, an offer will be provided in due course.
Contact:
If you require support with the administrative side of the application process, please contact mathematics-pgr@kcl.ac.uk
and Dr. Purba Das: (Email: Purba.das@kcl.ac.uk).