A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equation

Maxim Bichuch and Ke Chen

Chapter 4 in Peter Carr Gedenkschrift:Research Advances in Mathematical Finance, 2023, pp 101-140 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures (search for similar items in EconPapers)
JEL-codes: C02 C6 (search for similar items in EconPapers)
Date: 2023
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