4 Year GTA - Market Regime Switching and Metastability under Non-Gaussian Lévy Noise

About the Project

Open to UK Applicants only

Mathematics are offering 3 fully-funded Graduate Teaching Assistant (GTA) PhD studentships available for UK applicants, starting in September 2026.

Graduate Teaching Assistantships allow research students to fund their PhD through part-time teaching work with the University.

A Graduate Teaching Assistant is responsible to the Head of School and is expected to undertake teaching or other duties within the School - not normally exceeding 8-10 contact hours per week - while undertaking research leading to a PhD.

Approximately 80% of their time will be spent on their doctoral research and 20% on their GTA responsibilities. Training is provided to help Graduate Teaching Assistants develop their teaching related skills and enhance their professional competencies.

Project Highlights

• Novel Noise Modeling: Moves beyond traditional Gaussian frameworks by incorporating non-Gaussian Lévy noise to accurately capture the heavy tails and sudden discontinuous jumps inherent in real financial markets.
• Metastability Framework: Conceptualizes financial regimes (e.g., bull vs. bear markets) as metastable “potential wells,” providing a rigorous dynamical systems approach to understanding regime switching.
• Enhanced Risk Assessment: Calculates the Mean First Passage Time (MFPT) for market transitions, delivering mathematical proof that Lévy-based models provide superior crash probability estimations compared to classical Gaussian models.

Project description

Traditional financial models, relying heavily on Gaussian assumptions, fail to capture the empirical realities of financial markets, such as heavy tails, volatility clustering, and sudden discontinuous jumps. To address this limitation, this project proposes a novel framework for modeling market regime switching through the lens of metastability under non-Gaussian Lévy noise.

The research conceptualizes different market regimes, such as calm bull markets and turbulent bear markets—as metastable states within a stochastic dynamical system. By formulating stochastic differential equations (SDEs) driven by both Gaussian background noise and non-Gaussian Lévy jumps (e.g., Variance Gamma or NIG processes), the project maps market dynamics to a potential function representing fundamental value or market sentiment.

The core objective is to rigorously analyze the stability of these market equilibria and calculate the Mean First Passage Time (MFPT), the expected time for a market to abruptly escape a “stable” state and transition into a crisis regime. Methodologically, the project will combine analytical SDE techniques with advanced numerical simulations, including Monte Carlo methods and solutions to the Fractional Fokker-Planck equation, to estimate transition probabilities.

The expected results will yield a robust mathematical framework demonstrating that Lévy noise significantly accelerates escape times from metastable states compared to pure Gaussian noise. Consequently, the project will deliver approximation schemes for crash probabilities, proving that classical models systematically underestimate extreme event risks. Ultimately, this research will provide financial institutions with highly accurate, mathematically rigorous tools for enhanced risk management and crisis prediction, bridging the gap between theoretical stochastic analysis and practical financial stability.

Project enquiries to Dr. Larissa Serdukova Ls563@leicester.ac.uk

Application enquiries to pgrapply@le.ac.uk

To apply please refer to the application advice and use the application link at https://le.ac.uk/study/research-degrees/funded-opportunities/maths-gta

Start 21 September 2026

Funding Notes

The 4 year GTA funded studentships provide:

• A combined teaching and stipend payment, currently. for 2026/7 this will be £21,805 per year, paid in monthly instalments
• Tuition fees at UK rates