Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar assets as residual portfolios from conditional latent asset pricing factors. Second, we extract their time series signals with a powerful machine-learning time-series solution, a convolutional transformer. Lastly, we use these signals to form an optimal trading policy, that maximizes risk-adjusted returns under constraints. Our comprehensive empirical study on daily US equities shows a high compensation for arbitrageurs to enforce the law of one price. Our arbitrage strategies obtain consistently high out-of-sample mean returns and Sharpe ratios, and substantially outperform all benchmark approaches.
Statistical arbitrage is a class of financial trading strategies using mean reversion models. The corresponding techniques rely on a number of assumptions which may not hold for general non-stationary stochastic processes. This paper presents an alternative technique for statistical arbitrage based on online learning which does not require such assumptions and which benefits from strong learning guarantees.
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online Convex Optimization (OCO) framework, and present two algorithms that attain low regret. The first algorithm applies to Lipschitz continuous loss functions, obtaining optimal regret bounds for both convex and strongly convex losses. The second algorithm attains the optimal regret bounds and applies more broadly to convex losses without requiring Lipschitz co…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Virginia Tech（弗吉尼亚理工学院暨州立大学）；South China University of Technology（华南理工大学）
In this letter, we address the problem of controlling energy storage systems (ESSs) for arbitrage in real-time electricity markets under price uncertainty. We first formulate this problem as a Markov decision process, and then develop a deep reinforcement learning based algorithm to learn a stochastic control policy that maps a set of available information processed by a recurrent neural network to ESSs' charging/discharging actions. Finally, we verify the effectiveness of our algorithm using real-time electricity prices from PJM.
As the world seeks to become more sustainable, intelligent solutions are needed to increase the penetration of renewable energy. In this paper, the model-free deep reinforcement learning algorithm Rainbow Deep Q-Networks is used to control a battery in a small microgrid to perform energy arbitrage and more efficiently utilise solar and wind energy sources. The grid operates with its own demand and renewable generation based on a dataset collected at Keele University, as well as using dynamic energy pricing from a real wholesale energy market. Four scenarios are tested including using demand an…
Risk arbitrage or merger arbitrage is a well-known investment strategy that speculates on the success of M&A deals. Prediction of the deal status in advance is of great importance for risk arbitrageurs. If a deal is mistakenly classified as a completed deal, then enormous cost can be incurred as a result of investing in target company shares. On the contrary, risk arbitrageurs may lose the opportunity of making profit. In this paper, we present an ML and DL based methodology for takeover success prediction problem. We initially apply various ML techniques for data preprocessing such as kNN for…
UBS（瑞银集团）；Swiss Data Science Center（瑞士数据科学中心）；Columbia University（哥伦比亚大学）
We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft const…
IT University of Copenhagen（哥本哈根信息技术大学）；Technical University of Denmark（丹麦技术大学）
A lot of Machine Learning (ML) and Deep Learning (DL) research is of an empirical nature. Nevertheless, statistical significance testing (SST) is still not widely used. This endangers true progress, as seeming improvements over a baseline might be statistical flukes, leading follow-up research astray while wasting human and computational resources. Here, we provide an easy-to-use package containing different significance tests and utility functions specifically tailored towards research needs and usability.
Consistently checking the statistical significance of experimental results is one of the mandatory methodological steps to address the so-called "reproducibility crisis" in deep reinforcement learning. In this tutorial paper, we explain how the number of random seeds relates to the probabilities of statistical errors. For both the t-test and the bootstrap confidence interval test, we recall theoretical guidelines to determine the number of random seeds one should use to provide a statistically significant comparison of the performance of two algorithms. Finally, we discuss the influence of dev…
In this study, the effects of eight representation regularization methods are investigated, including two newly developed rank regularizers (RR). The investigation shows that the statistical characteristics of representations such as correlation, sparsity, and rank can be manipulated as intended, during training. Furthermore, it is possible to improve the baseline performance simply by trying all the representation regularizers and fine-tuning the strength of their effects. In contrast to performance improvement, no consistent relationship between performance and statistical characteristics wa…
McGill University（麦吉尔大学）；National Institute of Informatics（国立信息学研究所）
This paper proposes a deep denoising auto-encoder technique to extract better acoustic features for speech synthesis. The technique allows us to automatically extract low-dimensional features from high dimensional spectral features in a non-linear, data-driven, unsupervised way. We compared the new stochastic feature extractor with conventional mel-cepstral analysis in analysis-by-synthesis and text-to-speech experiments. Our results confirm that the proposed method increases the quality of synthetic speech in both experiments.
Traditional data quality control methods are based on users experience or previously established business rules, and this limits performance in addition to being a very time consuming process with lower than desirable accuracy. Utilizing deep learning, we can leverage computing resources and advanced techniques to overcome these challenges and provide greater value to users. In this paper, we, the authors, first review relevant works and discuss machine learning techniques, tools, and statistical quality models. Second, we offer a creative data quality framework based on deep learning and stat…
University of Missouri（密苏里大学）；University of Wollongong（伍伦贡大学）
Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning persp…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for sparse deep learning. In contrast to previous work, we consider different types of sparsity, such as few active connections, few active nodes, and other norm-based types of sparsity. Moreover, our theories cover important aspects that previous theories have neglected, such as multiple outputs, regularization, and l2-loss. The guarantees have a mild dependen…
George Mason University（乔治梅森大学）；University of Maryland, College Park（马里兰大学帕克分校）
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems. However, MCMC techniques are computationally challenging as they require several thousands of forward PDE solves. The goal of this paper is to introduce a fractional deep neural network based approach for the forward solves within an MCMC routine. Moreover, we discuss some approximation error estimates and illustrate the efficiency of our approach via sev…
In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning---pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the extraction of features from the training data as a margin criterion in a high-dimensional feature-vector space. The self-organized classifier is then supplied with small amounts of labelled data, as in deep learning. Although we employ a simple single-layer perceptron model, rather than directly analyzing a multi-layer neural network, we find a nontrivial phas…
