Research

Please see the homepage for a brief explanation of current research projects.

Research Interests

My research primarily focuses on Gaussian Processes (GPs), a Bayesian non-parametric modeling method, which I apply across various disciplines. I am particularly interested in the following areas:

• Gaussian Processes and Applications: Exploring novel covariance functions to enhance the expressivity and interpretability of GPs, enabling their use in diverse applications such as image super-resolution and advanced classification tasks in computer vision.

• Financial Mathematics and Quantitative Risk Management: Investigating GP-based techniques for risk assessment and option pricing, including quantile loss estimation and efficient Monte Carlo simulations. I am also interested in modeling liquidity dynamics in decentralized finance platforms and integrating GPs with stochastic volatility models.

• Actuarial Science and Mortality Modeling: Utilizing GPs and genetic algorithms to develop nuanced mortality models that capture age-period-cohort effects. This approach aims to improve the precision and interpretability of mortality forecasts essential for insurance and pension planning.

• Sports Analytics and Mathematical Finance: Creating innovative player valuation frameworks by combining financial models with network theory to assess player market values dynamically. Additionally, I explore the application of stochastic control methods to optimize team performance strategies throughout a season.

• Machine Learning and Data Science: Focusing on kernel expressivity and model interpretability within machine learning. I design novel covariance functions to better capture complex data structures, facilitating transparent and interpretable solutions in areas such as image processing and classification.

A key aspect of my research is bridging robust statistical methodologies with modern data-driven applications, ensuring that solutions are both transparent and interpretable.

Publications

• Book: Risk, Jimmy and Ludkovski, Michael. Gaussian Process Models for Quantitative Finance. In SpringerBriefs in Quantitative Finance Series, Springer. (In Press)
  • The first comprehensive treatment of Gaussian Processes in finance, this book includes extensive literature reviews, advanced methodologies, theoretical foundations, and computational strategies, serving as a vital resource for researchers and practitioners.
• Book Chapter: Risk, Jimmy and Ludkovski, Michael. Gaussian Processes for Statistical Learning in Actuarial Science. In Foundations for Undergraduate Research in Mathematics, Springer. (In Press)

Articles

• Risk, Jimmy, and Cohen, Albert. European Football Player Valuation: Integrating Financial Models and Network Theory. Journal of Quantitative Analysis in Sports (Accepted with Revision) arXiv link
• Risk, Jimmy, and Ludkovski, Michael. Expressive Mortality Models through Gaussian Process Kernels. ASTIN Bulletin: The Journal of the IAA 54.2 (2024): 327-359. arXiv link
• Risk, Jimmy, Switkes, Jennifer, and Zhang, Ann. N.C. Congressional Districting: A ‘Rocks-Pebbles-Sand Approach’. Discover Global Society 1.1 (2023): 18. arXiv link.
• Risk, Jimmy, Huynh, Nhan, and Ludkovski, Michael. SOA 2021 ILEC mortality prediction contest. Society of Actuaries (2021). www.soa.org/globalassets/assets/files/resources/research-report/2021/mort-prediction-contest.pdf
• Risk, Jimmy, and Ludkovski, Michael. Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement. SIAM Journal on Financial Mathematics 9.4 (2018) 1137-1174. arxiv link
• Ludkovski, Michael, Risk, Jimmy, and Zail, Howard. Gaussian Process Models for Mortality Rates and Improvement Factors. ASTIN Bulletin: The Journal of the IAA 48.3 (2018) 1307-1347. arxiv link
  • Accompanied R Notebook: github.com/jimmyrisk/GPmortalityNotebook
• Risk, Jimmy, and Ludkovski, Michael. Statistical emulators for pricing and hedging longevity risk products. Insurance: Mathematics and Economics 68 (2016): 45-60. arxiv link
• Risk, Jimmy. Correlations between Google search data and Mortality Rates. arXiv preprint arXiv:1209.2433 (2012). arxiv.org/abs/1209.2433

Preprints

• Risk, Jimmy, Tung, Shen-Ning, and Wang, Tai-Ho. Analysis and Forecasting of Liquidity Surfaces in Uniswap v3. (Working Paper)
• Cohen, Albert, Risk, Jimmy, and Wang, Tai-Ho. Stochastic Control Approaches to Dynamic Pythagorean Exponent Modelling in Sports Finance. (Working Paper)
• Cohen, Albert, Risk, Jimmy, and Wang, Tai-Ho. Dynamic Pythagorean Exponent Models and Option Pricing with Applications to Baseball. (Working Paper)
• Risk, Jimmy, Amelin, Charles, and Frank, Hakeem. Interpretable Kernels for Gaussian Process Super-Resolution. (Working Paper; To be submitted to IEEE Transactions on Image Processing)