A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equation
Abstract
We study the convergence of a deep learning algorithm applied to a general class of fully nonlinear second order Partial Differential Equations. By using a suitable finite difference approximation to the loss function of the deep learning scheme we show the convergence of the numerical solution to the unique viscosity solution. We apply our results and illustrate this convergence to the finite horizon optimal investment problem with proportional transaction costs in single and multi-asset settings.
Watch recording ↗About the speaker
Maxim Bichuch holds a M.S. from NYU and a Ph.D. from CMU both in Financial Mathematics. He has been a Postdoctoral Research Associate & Lecturer in the ORFE department in Princeton, and an Assistant Professor at WPI and JHU, before joining the department of Mathematics at UB. Prior to obtaining his Ph.D. He has also gained corporate experience working for Citigroup and Bear Stearns. His research interests include optimal portfolio selection, optimal investment and consumption, optimal control with transaction costs, viscosity solutions, stochastic volatility, credit, funding and counterparty risks, and most recently electricity markets, machine learning, decentralized finance and fintech.