Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high\n dimensional BSDEs

2017/10/19 by Masaaki Fujii, Fujii, Masaaki, Akihiko Takahashi +3
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Capital Investment and Risk Analysis #Financial Markets and Investment Strategies

paper · pdf · doi:10.48550/arxiv.1710.07030

Abstract

We demonstrate that the use of asymptotic expansion as prior knowledge in the\n"deep BSDE solver", which is a deep learning method for high dimensional BSDEs\nproposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss\nfunction and accelerates the speed of convergence. We illustrate the technique\nand its implications by using Bergman's model with different lending and\nborrowing rates as a typical model for FVA as well as a class of solvable BSDEs\nwith quadratic growth drivers. We also present an extension of the deep BSDE\nsolver for reflected BSDEs representing American option prices.\n

Related

• Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing
• A deep solver for BSDEs with jumps
• Deep-learning based numerical BSDE method for barrier options
• Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions
• Towards Robust and Stable Deep Learning Algorithms for Forward Backward\n Stochastic Differential Equations