Modul:   MAT959  Seminar in Data Science and Mathematical Modelling

Deep Learning based algorithm for nonlinear PDEs in finance and gradient descent type algorithm for non-convex stochastic optimization problems with ReLU neural networks

Vortrag von Prof. Dr. Ariel Neufeld

Sprecher eingeladen von: Prof. Dr. Delia Marina Coculescu

Datum: 05.10.23  Zeit: 12.15 - 13.45  Raum: Y27H12

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.