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This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage…

Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…

Neural networks work remarkably well in practice and theoretically they can be universal approximators. However, they still make mistakes and a specific type of them called adversarial errors seem inexcusable to humans. In this work, we…

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set…

Prediction markets show considerable promise for developing flexible mechanisms for machine learning. Here, machine learning markets for multivariate systems are defined, and a utility-based framework is established for their analysis. This…

In this paper, we examine the capacity of an arbitrage-free neural-SDE market model to produce realistic scenarios for the joint dynamics of multiple European options on a single underlying. We subsequently demonstrate its use as a risk…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…

We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…

Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…

Neural network controllers have shown potential in achieving superior performance in feedback control systems. Although a neural network can be trained efficiently using deep and reinforcement learning methods, providing formal guarantees…

In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…

Recently, there is growing concern that machine-learning models, which currently assist or even automate decision making, reproduce, and in the worst case reinforce, bias of the training data. The development of tools and techniques for…

In this paper, we propose a new procedure for unconditional and conditional forecasting in agent-based models. The proposed algorithm is based on the application of amortized neural networks and consists of two steps. The first step…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…

We initiate the study of deep learning for the automated design of two-sided matching mechanisms. What is of most interest is to use machine learning to understand the possibility of new tradeoffs between strategy-proofness and stability.…

Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…