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We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with model selection., Comment: 51 pages, 4 figures

We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher precision quantum estimates of the eigenvalues relevant to the linear system, and a new classical step to guide the eigenvalue inversion part of Hybrid HHL. We show that eigenvalue estimates with just two extra bits of precision result in tighter error bounds for our Enhanced Hybrid HHL compared to HHL. Our enhancement reduces the error of Hybrid HHL by an average of 57 percent on an ideal quantum processor for a representative sample of 2x2 systems. On IBM Torino and IonQ Aria-1 hardware, we see that the error of Enhanced Hybrid HHL is on average 13 percent and 20 percent (respectively) less than that of HHL for the same set of systems., Comment: 27 pages, 4 figures, submitted to Physics Letters A

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both realistic in terms of mimicking financial market risks as well as more amenable to potential quantum computational advantages. The type of models we study are based on a regime switching volatility model driven by a Markov chain with observable states. The basic model features a Geometric Brownian Motion with drift and volatility parameters determined by the finite states of a Markov chain. We study algorithms to estimate credit risk and option pricing on a gate-based quantum computer. These models bring us closer to realistic market settings, and therefore quantum computing closer the realm of practical applications.

This paper surveys the recent advances in machine learning method for economic forecasting. The survey covers the following topics: nowcasting, textual data, panel and tensor data, high-dimensional Granger causality tests, time series cross-validation, classification with economic losses.

The paper uses structured machine learning regressions for nowcasting with panel data consisting of series sampled at different frequencies. Motivated by the problem of predicting corporate earnings for a large cross-section of firms with macroeconomic, financial, and news time series sampled at different frequencies, we focus on the sparse-group LASSO regularization which can take advantage of the mixed frequency time series panel data structures. Our empirical results show the superior performance of our machine learning panel data regression models over analysts' predictions, forecast combinations, firm-specific time series regression models, and standard machine learning methods., Comment: arXiv admin note: substantial text overlap with arXiv:2008.03600

In this paper, we develop new methods for analyzing high-dimensional tensor datasets. A tensor factor model describes a high-dimensional dataset as a sum of a low-rank component and an idiosyncratic noise, generalizing traditional factor models for panel data. We propose an estimation algorithm, called tensor principal component analysis (TPCA), which generalizes the traditional PCA applicable to panel data. The algorithm involves unfolding the tensor into a sequence of matrices along different dimensions and applying PCA to the unfolded matrices. We provide theoretical results on the consistency and asymptotic distribution for the TPCA estimator of loadings and factors. We also introduce a novel test for the number of factors in a tensor factor model. The TPCA and the test feature good performance in Monte Carlo experiments and are applied to sorted portfolios.

We study the binary choice problem in a data-rich environment with asymmetric loss functions. The econometrics literature covers nonparametric binary choice problems but does not offer computationally attractive solutions in data-rich environments. The machine learning literature has many algorithms but is focused mostly on loss functions that are independent of covariates. We show that theoretically valid decisions on binary outcomes with general loss functions can be achieved via a very simple loss-based reweighting of the logistic regression or state-of-the-art machine learning techniques. We apply our analysis to racial justice in pretrial detention.

The paper introduces structured machine learning regressions for heavy-tailed dependent panel data potentially sampled at different frequencies. We focus on the sparse-group LASSO regularization. This type of regularization can take advantage of the mixed frequency time series panel data structures and improve the quality of the estimates. We obtain oracle inequalities for the pooled and fixed effects sparse-group LASSO panel data estimators recognizing that financial and economic data can have fat tails. To that end, we leverage on a new Fuk-Nagaev concentration inequality for panel data consisting of heavy-tailed $\tau$-mixing processes.

This paper introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and outperforms the unstructured LASSO. We establish oracle inequalities for the sparse-group LASSO estimator within a framework that allows for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier than exponential tails. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that text data can be a useful addition to more traditional numerical data., Comment: Portions of this work previously appeared as arXiv:1912.06307v1 which has been split into two articles

We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and develop the inferential theory in the high-dimensional setting. To recognize the time series data structures we focus on the sparse-group LASSO estimator, which includes the LASSO and the group LASSO as special cases. We establish the debiased central limit theorem for low dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sparse-group LASSO residuals. This leads to valid time series inference for individual regression coefficients as well as groups, including Granger causality tests. The treatment relies on a new Fuk-Nagaev inequality for a class of $\tau$-mixing processes with heavier than Gaussian tails, which is of independent interest. In an empirical application, we study the Granger causal relationship between the VIX and financial news.

Artificial intelligence, or AI, enhancements are increasingly shaping our daily lives. Financial decision-making is no exception to this. We introduce the notion of AI Alter Egos, which are shadow robo-investors, and use a unique data set covering brokerage accounts for a large cross-section of investors over a sample from January 2003 to March 2012, which includes the 2008 financial crisis, to assess the benefits of robo-investing. We have detailed investor characteristics and records of all trades. Our data set consists of investors typically targeted for robo-advising. We explore robo-investing strategies commonly used in the industry, including some involving advanced machine learning methods. The man versus machine comparison allows us to shed light on potential benefits the emerging robo-advising industry may provide to certain segments of the population, such as low income and/or high risk averse investors.