Abstract: In this talk, we introduce a Banach space-valued extension of random feature learning, which we apply to random neural networks as particular instance. This allows us to lift the universal approximation property of deterministic neural networks to random neural networks, where the approximation of the derivatives can now be included. Building on these theoretical insights, we propose a randomized extension of the deep splitting algorithm to solve high-dimensional non-linear parabolic P(I)DEs more efficiently, which is useful for pricing financial derivatives under default risk and in the presence of jumps with (possibly) infinite activity. Additionally, we approximate the solution of certain SPDEs by using random neural networks in the truncated Wiener chaos expansion, which allows us to learn the solution of, e.g., the Heath-Jarrow-Morton equation in interest rate theory.

This talk is based on joint works with Ariel Neufeld and Sizhou Wu.

Bio: Philipp is a Ph.D. student in Mathematics at Nanyang Technological University (NTU), Singapore, under the supervision of Prof. Dr. Ariel Neufeld. His research focuses on machine learning applications in mathematical finance, with a particular emphasis on neural networks. Philipp holds a B.Sc. (2016) and an M.Sc. (2017) in Mathematics from ETH Zurich, as well as a Ph.D. in Economics and Finance (2022) from the University of St. Gallen.

Meeting Recording: https://ucsb.zoom.us/rec/share/KMKZKP7FxfNADCtzuIsOU30vT-NEZIjocAa41EYujRxlF9sjjhPNJD5LHqHQx-su.IiAHzwE3CWEFUuye

Access Passcode: $P?5TNOf