Mathematics: UKRI and Swansea University Funded PhD Scholarship: Optimal Problems Under Contagious Markets with Regime Switching and Risk Uncertainty (RS648)

  • DeadlineDeadline: 1 August 2024
  • WalesWales


Closing date: 1 August 2024

Funding provider(s): UKRI and Faculty of Science and Engineering 

Subject area(s): Stochastic Optimal Controls, Point Processes, insurance strategies, regime switchings, and Risk Uncertainty

Project start date(s):

  • 1 October 2024   
  • 1 January 2025 

Supervisors: Guo Liu and Chenggui Yuan 

Aligned programme of study:  PhD in Mathematics

Mode of study: Full-time 

Project description: 

In this project, different optimal control problems will be considered under a contagious financial and insurance market with regime switching and risk uncertainty. 

In the first chapter, an optimal portfolio choice and life consumption problem will be studied under a fragile financial market with regime switching and risk uncertainty, where the transition matrix is no longer constant but depends on historical paths of financial assets in that market. 

In the second chapter, an optimal re-insurance problem will be investigated under a contagious insurance market with regime switching. A stochastic differential game will be constructed to find the optimal reinsurance policy by considering the interaction between the insurer and the reinsurer. 

More chapters will be considered if the first two chapters run smoothly. 

For more details please see here:

Entry Requirements

Candidates must hold a UK Bachelor degree with a minimum of Upper Second Class honours in Computer Science, Mathematics or a closely related discipline or overseas Bachelor degree deemed equivalent to UK Bachelor (by UK ECCTIS) and achieved a grade equivalent to UK Upper Second Class honours in Computer Science, Mathematics or a closely related discipline;

Or an appropriate master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University)  – see country specific qualifications.

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by  UKCISA regulations.

Please note that you may need to provide evidence of your English Language proficiency.

If you have any questions regarding your academic or fee eligibility based on the above, please email with the web-link to the scholarship(s) you are interested in. 


This scholarship covers the full cost of UK tuition fees and an annual stipend of £19,237.

Additional research expenses of up to £1000 per year will also be available.

How To Apply

To apply, please complete your application online with the following information:

  1. Course choice – please select Mathematics / PhD / Full-time / 3 Years / October OR
    for January 2025 start select:
    Mathematics/ PhD / Full-time / 3 Years / January 

    In the event you have already applied for the above programme previously, the application system may issue a warning notice and prevent application. In this event, please email where staff will be happy to assist you in submitting your application.

  2. Start year – please select 2024
  3. Funding (page 8) –
  • ‘Are you funding your studies yourself?’ – please select No
  • ‘Name of Individual or organisation providing funds for study’ – please enter ‘RS648 - Risk Uncertainty’

*It is the responsibility of the applicant to list the above information accurately when applying, please note that applications received without the above information listed will not be considered for the scholarship award.

One application is required per individual Swansea University led research scholarship award; applications cannot be considered listing multiple Swansea University led research scholarship awards.

We encourage you to complete the following to support our commitment to providing an environment free of discrimination and celebrating diversity at Swansea University: 

As part of your online application, you MUST upload the following documents (please do not send these via email). We strongly advise you to provide the listed supporting documents by the advertised closing date, where possible:

  • CV
  • Degree certificates and transcripts (if you are currently studying for a degree, screenshots of your grades to date are sufficient)
  • A cover letter including a ‘Supplementary Personal Statement’ to explain why the position particularly matches your skills and experience and how you choose to develop the project.
  • Two references (academic or previous employer) on headed paper or using the Swansea University reference form. Please note that we are not able to accept references received citing private email accounts, e.g. Hotmail. Referees should cite their employment email address for verification of reference.
  • Evidence of meeting English Language requirement (if applicable).
  • Copy of UK resident visa (if applicable)
  • Confirmation of EDI form submission (optional) 

Informal enquiries are welcome; please contact Dr Guo Liu (  / (+44)1792 513 050).

*External Partner Application Data Sharing – Please note that as part of the scholarship application selection process, application data sharing may occur with external partners outside of the University, when joint/co- funding of a scholarship project is applicable.

Who is eligible to apply?

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations. 

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