Gaussian Process Models for Quantitative Finance

Mike Ludkovski is a Professor of Statistics and Applied Probability at University of California Santa Barbara. He was Department Chair during 2018-2022 and since 2016 is a Co-Director of the Center for Financial Mathematics and Actuarial Research. He has 15+ years of experience and 80+ publications in stochastic modeling of energy markets, numerical methods for stochastic control and predictive analytics. Among his current research interests are Monte Carlo techniques for optimal stopping/stochastic control, non-zero-sum stochastic games, and applications of machine learning in longevity and non-life insurance. He serves on 5+ Editorial Boards and his research has been funded by NSF, ARPA-E and Society of Actuaries. During 2015-2016 he was Chair of the SIAM Activity Group on Financial Mathematics & Engineering. He co-edited the volume on "Commodities, Energy and Environmental Finance" (2015). Ludkovski holds a Ph.D. in Operations Research and Financial Engineering from Princeton University and has held visiting positions at London School of Economics and Paris Dauphine University.

Jimmy Risk is an Assistant Professor of Mathematics and Statistics at California Polytechnic State University Pomona. He was temporary chair during Summer 2022 and has advised nine master's thesis students since taking his position in Fall 2017, several of which involving applications of Gaussian processes in modern data science including neural networks, natural language processing, and super-resolution. His education involves a Ph.D. in Statistics and Applied Probability with an emphasis in Financial Mathematics from University of California Santa Barbara, which has driven publications involving pricing and tail risk analysis using Gaussian processes to approximate conditional expectations. Additionally, Risk has an extensive actuarial science background, including developing a Gaussian process model for mortality rates, and more recently winning an open international mortality prediction contest held by the Society of Actuaries alongside Mike Ludkovski. Risk's recent research interests involve the theory and applications of Gaussian process kernels, which lie in the Reproducing Kernel Hilbert Space framework.

- 1. Gaussian Process Preliminaries.- 2. Covariance Kernels.- 3. Advanced GP Modeling Topics.- 4. Option Pricing and Sensitivities.- 5. Optimal Stopping.- 6. Non-Parametric Modeling of Financial Structures.- 7. Stochastic Control.