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Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…

Deep learning has excelled in image recognition tasks through neural networks inspired by the human brain. However, the necessity for large models to improve prediction accuracy introduces significant computational demands and extended…

In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…

The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach.…

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…

Stock market prediction has been a classical yet challenging problem, with the attention from both economists and computer scientists. With the purpose of building an effective prediction model, both linear and machine learning tools have…

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

Differential machine learning combines automatic adjoint differentiation (AAD) with modern machine learning (ML) in the context of risk management of financial Derivatives. We introduce novel algorithms for training fast, accurate pricing…

This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…

Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box' nature also results in a lack of interpretability. We…

We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the…

In recent years, the power demonstrated by Machine Learning (ML) has increasingly attracted the interest of the optimization community that is starting to leverage ML for enhancing and automating the design of algorithms. One combinatorial…

Experience has shown that trading in stock and cryptocurrency markets has the potential to be highly profitable. In this light, considerable effort has been recently devoted to investigate how to apply machine learning and deep learning to…

Differential ML (Huge and Savine 2020) is a technique for training neural networks to provide fast approximations to complex simulation-based models for derivatives pricing and risk management. It uses price sensitivities calculated through…

We predict asset returns and measure risk premia using a prominent technique from artificial intelligence -- deep sequence modeling. Because asset returns often exhibit sequential dependence that may not be effectively captured by…

This paper contributes to the literature on parametric demand estimation by using deep learning to model consumer preferences. Traditional econometric methods often struggle with limited within-product price variation, a challenge addressed…

We study a classification problem where each feature can be acquired for a cost and the goal is to optimize a trade-off between the expected classification error and the feature cost. We revisit a former approach that has framed the problem…

We study the problem of collaborative machine learning markets where multiple parties can achieve improved performance on their machine learning tasks by combining their training data. We discuss desired properties for these machine…

Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…