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 based modeling method, which I have utilized across various disciplines. These include:

• Financial Mathematics and Sports Analytics: My exploration in financial mathematics, particularly in the quantile of loss estimation and pricing, seamlessly extends into the realm of sports analytics. This interdisciplinary approach has led to innovative frameworks in player valuation in soccer, blending financial models with network theory to assess player market values.
• Actuarial Science: In mortality modeling and pricing, I have recently delved into using GPs and genetic algorithms for qualitatively assessing mortality populations. This innovative approach allows for a more nuanced understanding of mortality trends, enhancing the precision and interpretability of actuarial models.
• Modern Machine Learning Tasks: My work encompasses a range of machine learning applications, from super-resolution and computer vision classification to analyzing the roles of kernels in machine learning tasks.

A significant aspect of my research is to bridge well-founded methodologies in probability and statistics with modern data science challenges. Unlike the black box nature of neural networks, Gaussian processes, through their kernel structure, provide insights into the properties of the function being modeled, such as differentiability, continuity, and periodicity. This approach underlines my commitment to developing transparent, interpretable, and robust solutions to state-of-the-art problems in data science.

Publications

• Risk, Jimmy, and Ludkovski, Michael. Expressive Mortality Models through Gaussian Process Kernels. ASTIN Bulletin: The Journal of the IAA 48.3 (Accepted With Revision Aug 23). arXiv link
• Risk, Jimmy, Switkes, Jennifer, and Zhang, Ann. N.C. Congressional Districting: A ‘Rocks-Pebbles-Sand Approach’. Discover Global Society (To Appear 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, and Cohen, Albert. Stochastic Modeling of Soccer Player Valuation Using Network Theory and Financial Mathematics. (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.)

Books and Book Chapters

• Book Chapter: Risk, Jimmy and Ludkovski, Michael. Gaussian Processes for Statistical Learning in Actuarial Science. In Foundations for Undergraduate Research in Mathematics, Springer. (Rough Draft Completed, Fall 2023)
• Book: Risk, Jimmy. Gaussian Process Models in Quantitative Finance. In SpringerBriefs in Quantitative Finance Series, Springer. (Proposal Accepted Spring 2023; Work in progress)