Stochastic Optimal Controls: Optimal problems under contagious markets with regime switching and risk uncertainty (RS822)

Funding providers: UKRI and Faculty of Science and Engineering 

Subject areas: Stochastic Optimal Controls, Point Processes, Insurance Strategies, Regime Switchings, and Risk Uncertainty  

Project start date: 1 July 2025

Supervisors: Dr Guo Liu and Professor Chenggui Yuan 

Aligned programme of study: PhD in Mathematics 

Mode of study: Full-time 

Funding Duration: 3 years

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 reinsurance 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.   

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 

Applicants for PhD must hold an undergraduate degree at 2.1 level or master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University).  See 2025-Country-Specific-Entry-Requirement-document-MASTER.pdf 

English Language 

IELTS 6.0 Overall (with no individual component below 5.5) or Swansea University recognised equivalent. Full details of our English Language policy, including certificate time validity, can be found here.  

This scholarship covers the full cost of tuition fees and an annual stipend at UKRI rate (currently £19,237 for 2024/25). 

Additional research expenses of up to £1,000 per year will also be available. 

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

1. Course choice – please select as per preferred mode of study: (Full Time) Mathematics / PhD / Full-time / 3 Years / July 
   • 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 pgrscholarships@swansea.ac.uk where staff will be happy to assist you in submitting your application. 
2. Start year – please select 2025 
3. Funding (page 8 on the application process):

• ‘Are you funding your studies yourself?’ – please select No 

• ‘Name of Individual or organisation providing funds for study’ – please enter  ‘RS822 - 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. 

NOTE: Applicants for PhD/EngD/ProfD/EdD - to support our commitment to providing an environment free of discrimination and celebrating diversity at Swansea University you are required to complete an Equality, Diversity and Inclusion (EDI) Monitoring Form in addition to your programme application form.    

Please note that completion of the EDI Monitoring Form is mandatory; your application may not progress if this information is not submitted. 

As part of your online application, you MUST upload the following documents (please do not send these via email): 

• 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. 

• One reference (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 

Informal enquiries are welcome; please contact  Guo Liu – guo.liu@swansea.ac.uk 

*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.