Abstract: In this talk, we first present a deep-learning based algorithm which can solve nonlinear parabolic PDEs in up to 10,000 dimensions with short run times, and apply it to price high-dimensional financial derivatives under default risk. Then, we discuss a general problem when training neural networks, namely that it typically involves non-convex stochastic optimization. To that end, we present TUSLA, a gradient descent type algorithm (or more precisely: stochastic gradient Langevin dynamics algorithm) for which we can prove that it can solve non-convex stochastic optimization problems involving ReLU neural networks.

This talk is based on joint works with C. Beck, S. Becker, P. Cheridito, A. Jentzen, and D.-Y. Lim, S. Sabanis, Y. Zhang, respectively.

Bio: Ariel Neufeld obtained his PhD in 2015 under the joint supervision of Martin Schweizer (ETH Zurich) and Marcel Nutz (Columbia University). After continuing as a PostDoc at ETH Zurich under Mete Soner, Patrick Cheridito, and Arnulf Jentzen, he joined the Nanyang Technological University in January 2019 as Nanyang Assistant Professor. His research focuses on model uncertainty in financial markets, stochastic optimal control theory, as well as modern (also deep learning based) numerical methods for finance and insurance.

Meeting Recording: https://ucsb.zoom.us/rec/share/s9YDMvvjPkHLDA5FX2jSQBLqyekNnorUQW_HKR9OH5RiEuYVPbz__XsOtEOt6GF_.FEb9rohMbGUvW838

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