Yuri Saporito (FGV, Rio de Janeiro, Brazil)

Machine Learning Techniques in Finance

We will discuss two new applications of Machine Learning in Finance:

1) In this work we present a methodology for numerically solving a wide class of partial differential equations (PDEs) and PDE systems using deep neural networks. The PDEs we consider are related to various applications in quantitative finance including option pricing, optimal investment and the study of mean field games and systemic risk. The numerical method is based on the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos with modifications made depending on the application of interest. This project won the Financial Mathematics Team Challenge Brazil (FMTC BR) 2018. The team members were Ali Al-Aradi (team leader, University of Toronto), Adolfo Correia (IMPA), Danilo Naiff (IM/UFRJ) and Gabriel Jardim (FGV EMAp).

2) We proposed a novel non-parametric method to solve inverse problems. The method is based on the Gradient Boosting from the statistical learning literature. The smoothness (using smooth boosts) and robustness of the method generates well-behaved solutions to inverse problems. We will apply the method to the estimation of local volatility functions, a very well-known problem in Quantitative Finance. The method generates well-behaved local volatility surfaces, capable of replicating vanilla option prices and the implied volatility surface.