In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population.

In this note I show that quadratic funding achieves decentralized social efficiency in the extent there are enough (donor) matching funds to cover the quadratic funding objective. If individual backers internalize that matching funds will not be sufficient to reach the quadratic level, allocation will be biased towards the capitalist allocation, the more so, the less matching funds are available. This result emerges even when individual contributors are not required to finance the deficit (i.e., the difference between total contributions and available matching funds). I also show properties of the level of required matching fund, in order to better understand under which conditions social efficiency will most likely be compromised.

Genetic programming (GP) is the state-of-the-art in financial automated feature construction task. It employs reverse polish expression to represent features and then conducts the evolution process. However, with the development of deep learning, more powerful feature extraction tools are available. This paper proposes Alpha Discovery Neural Network (ADNN), a tailored neural network structure which can automatically construct diversified financial technical indicators based on prior knowledge. We mainly made three contributions. First, we use domain knowledge in quantitative trading to design the sampling rules and object function. Second, pre-training and model pruning has been used to replace genetic programming, because it can conduct more efficient evolution process. Third, the feature extractors in ADNN can be replaced by different feature extractors and produce different functions. The experiment results show that ADNN can construct more informative and diversified features than GP, which can effectively enriches the current factor pool. The fully-connected network and recurrent network are better at extracting information from the financial time series than the convolution neural network. In real practice, features constructed by ADNN can always improve multi-factor strategies' revenue, sharpe ratio, and max draw-down, compared with the investment strategies without these factors.

In automatic financial feature construction task, the state-of-the-art technic leverages reverse polish expression to represent the features, then use genetic programming (GP) to conduct its evolution process. In this paper, we propose a new framework based on neural network, alpha discovery neural network (ADNN). In this work, we made several contributions. Firstly, in this task, we make full use of neural network overwhelming advantage in feature extraction to construct highly informative features. Secondly, we use domain knowledge to design the object function, batch size, and sampling rules. Thirdly, we use pre-training to replace the GP evolution process. According to neural network universal approximation theorem, pre-training can conduct a more effective and explainable evolution process. Experiment shows that ADNN can remarkably produce more diversified and higher informative features than GP. Besides, ADNN can serve as a data augmentation algorithm. It further improves the the performance of financial features constructed by GP.

The purpose of this paper is to review the concept of cryptocurrencies in our economy. First, Bitcoin and alternative cryptocurrencies' histories are analyzed. We then study the implementation of Bitcoin in the airline and real estate industries. Our study finds that many Bitcoin companies partner with airlines in order to decrease processing times, to provide ease of access for spending in international airports, and to reduce fees on foreign exchanges for fuel expenses, maintenance, and flight operations. Bitcoin transactions have occurred in the real estate industry, but many businesses are concerned with Bitcoin's potential interference with the U.S. government and its high volatility. As Bitcoin's price has been growing rapidly, we assessed Bitcoin's real value; Bitcoin derives value from its scarcity, utility, and public trust. In the conclusion, we discuss Bitcoin's future and conclude that Bitcoin may change from a short-term profit investment to a more steady industry as we identify Bitcoin with the "greater fool theory", and as the number of available Bitcoins to be mined dwindles and technology becomes more expensive.

We study deep learning-based schemes for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). First we show how to improve the performances of the proposed scheme in [W. E and J. Han and A. Jentzen, Commun. Math. Stat., 5 (2017), pp.349-380] regarding computational time and stability of numerical convergence by using the advanced neural network architecture instead of the stacked deep neural networks. Furthermore, the proposed scheme in that work can be stuck in local minima, especially for a complex solution structure and longer terminal time. To solve this problem, we investigate to reformulate the problem by including local losses and exploit the Long Short Term Memory (LSTM) networks which are a type of recurrent neural networks (RNN). Finally, in order to study numerical convergence and thus illustrate the improved performances with the proposed methods, we provide numerical results for several 100-dimensional nonlinear BSDEs including a nonlinear pricing problem in finance.

This paper shows that temporal CNNs accurately predict bitcoin spot price movements from limit order book data. On a 2 second prediction time horizon we achieve 71\% walk-forward accuracy on the popular cryptocurrency exchange coinbase. Our model can be trained in less than a day on commodity GPUs which could be installed into colocation centers allowing for model sync with existing faster orderbook prediction models. We provide source code and data at https://github.com/Globe-Research/deep-orderbook.

Modern machine learning models (such as deep neural networks and boosting decision tree models) have become increasingly popular in financial market prediction, due to their superior capacity to extract complex non-linear patterns. However, since financial datasets have very low signal-to-noise ratio and are non-stationary, complex models are often very prone to overfitting and suffer from instability issues. Moreover, as various machine learning and data mining tools become more widely used in quantitative trading, many trading firms have been producing an increasing number of features (aka factors). Therefore, how to automatically select effective features becomes an imminent problem. To address these issues, we propose DoubleEnsemble, an ensemble framework leveraging learning trajectory based sample reweighting and shuffling based feature selection. Specifically, we identify the key samples based on the training dynamics on each sample and elicit key features based on the ablation impact of each feature via shuffling. Our model is applicable to a wide range of base models, capable of extracting complex patterns, while mitigating the overfitting and instability issues for financial market prediction. We conduct extensive experiments, including price prediction for cryptocurrencies and stock trading, using both DNN and gradient boosting decision tree as base models. Our experiment results demonstrate that DoubleEnsemble achieves a superior performance compared with several baseline methods.

In this paper, company investment value evaluation models are established based on comprehensive company information. After data mining and extracting a set of 436 feature parameters, an optimal subset of features is obtained by dimension reduction through tree-based feature selection, followed by the 5-fold cross-validation using XGBoost and LightGBM models. The results show that the Root-Mean-Square Error (RMSE) reached 3.098 and 3.059, respectively. In order to further improve the stability and generalization capability, Bayesian Ridge Regression has been used to train a stacking model based on the XGBoost and LightGBM models. The corresponding RMSE is up to 3.047. Finally, the importance of different features to the LightGBM model is analysed.

We provide closed-form pricing formulas for a wide variety of path-independent options, in the exponential L\'evy model driven by the Normal inverse Gaussian process. The results are obtained in both the symmetric and asymmetric model, and take the form of simple and quickly convergent series, under some condition involving the log-forward moneyness and the maturity of instruments. Proofs are based on a factorized representation in the Mellin space for the price of an arbitrary path-independent payoff, and on tools from complex analysis. The validity of the results is assessed thanks to several comparisons with standard numerical methods (Fourier and Fast Fourier transforms, Monte-Carlo simulations) for realistic sets of parameters. Precise bounds for the convergence speed and the truncation error are also provided.

We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising expected utility in this setting. Besides establishing the existence of optimizers under weaker assumptions than previous papers, we go on studying the relationship between optimal investments in finite market segments and those in the whole market. We show that certain natural (but nontrivial) continuity rules hold: maximal satisfaction, reservation prices and (convex combinations of) optimizers computed in small markets converge to their respective counterparts in the big market.

Pairs trading is a strategy based on exploiting mean reversion in prices of securities. It has been shown to generate significant excess returns, but its profitability has dropped significantly in recent periods. We employ the most common distance and cointegration methods on US equities from 1990 to 2020 including the Covid-19 crisis. The strategy overall fails to outperform the market benchmark even with hyperparameter tuning, but it performs very strongly during bear markets. Furthermore, we demonstrate that market factors have a strong relationship with the optimal parametrization for the strategy, and adjustments are appropriate for modern market conditions.

We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures.

The Glosten-Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szil\'ard information engine by {\em i)} showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and {\em ii)} defining a market analogue of the physical temperature from the analysis of the distribution of market orders. Then we show that the expected gain of informed traders is bounded above by the product of this market temperature with the amount of information that informed traders have, in exact analogy with the corresponding formula for the maximal expected amount of work that can be extracted from a cycle of the information engine. In this way, recent ideas from information thermodynamics may shed light on financial markets, and lead to generalised inequalities, in the spirit of the extended second law of thermodynamics.

The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of passive investing, it still has shortcomings in real-world applications. One of the main challenges is that the level of risk an investor can endure, known as \emph{risk-preference}, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from existing portfolios using inverse optimization on the mean-variance portfolio allocation framework. Our approach allows the learner to continuously estimate real-time risk preferences using concurrent observed portfolios and market price data. We demonstrate our methods on real market data that consists of 20 years of asset pricing and 10 years of mutual fund portfolio holdings. Moreover, the quantified risk preference parameters are validated with two well-known risk measurements currently applied in the field. The proposed methods could lead to practical and fruitful innovations in automated/personalized portfolio management, such as Robo-advising, to augment financial advisors' decision intelligence in a long-term investment horizon.

More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was detected in the empirical distributions of the relative returns. Moreover, a number of new power law behaviors with various power exponents were explored in the same data. Further on, a model based on finite sums over numerous Maxwell-Boltzmann type distribution functions with random (pseudorandom) multipliers in the exponent were proposed to deal with the empirical distributions involving power laws. The results indicate that the proposed model may be universal.

Combinations of neural ODEs with recurrent neural networks (RNN), like GRUODE-Bayes or ODE-RNN are well suited to model irregularly-sampled time series. While those models outperform existing discrete-time approaches, no theoretical guarantees for their predictive capabilities are available. Assuming that the irregularly-sampled time series data originates from a continuous stochastic processes, the optimal on-line prediction is the conditional expectation given the currently available information. We introduce the Neural Jump ODE (NJ-ODE) that provides a data-driven approach to learn, continuously in time, the conditional expectation of a stochastic process. Our approach models the conditional expectation between two observations with a neural ODE and jumps whenever a new observation is made. We define a novel training framework, which allows us to prove theoretical convergence guarantees for the first time. In particular, we demonstrate the predictive capabilities of our model by proving that, under some regularity assumptions, the output process converges to the conditional expectation process. We provide experiments showing that the theoretical results also hold empirically. Moreover, we experimentally show that our model outperforms one state of the art model in more complex learning tasks and give comparisons on a real-world dataset.

Instead of conducting manual factor construction based on traditional and behavioural finance analysis, academic researchers and quantitative investment managers have leveraged Genetic Programming (GP) as an automatic feature construction tool in recent years, which builds reverse polish mathematical expressions from trading data into new factors. However, with the development of deep learning, more powerful feature extraction tools are available. This paper proposes Neural Network-based Automatic Factor Construction (NNAFC), a tailored neural network framework that can automatically construct diversified financial factors based on financial domain knowledge and a variety of neural network structures. The experiment results show that NNAFC can construct more informative and diversified factors than GP, to effectively enrich the current factor pool. For the current market, both fully connected and recurrent neural network structures are better at extracting information from financial time series than convolution neural network structures. Moreover, new factors constructed by NNAFC can always improve the return, Sharpe ratio, and the max draw-down of a multi-factor quantitative investment strategy due to their introducing more information and diversification to the existing factor pool.

Optimal execution, i.e., the determination of the most cost-effective way to trade volumes in continuous trading sessions, has been a topic of interest in the equity trading world for years. Electricity intraday trading slowly follows this trend but is far from being well-researched. The underlying problem is a very complex one. Energy traders, producers, and electricity wholesale companies receive various position updates from customer businesses, renewable energy production, or plant outages and need to trade these positions in intraday markets. They have a variety of options when it comes to position sizing or timing. Is it better to trade all amounts at once? Should they split orders into smaller pieces? Taking the German continuous hourly intraday market as an example, this paper derives an appropriate model for electricity trading. We present our results from an out-of-sample study and differentiate between simple benchmark models and our more refined optimization approach that takes into account order book depth, time to delivery, and different trading regimes like XBID (Cross-Border Intraday Project) trading. Our paper is highly relevant as it contributes further insight into the academic discussion of algorithmic execution in continuous intraday markets and serves as an orientation for practitioners. Our initial results suggest that optimal execution strategies have a considerable monetary impact.

We develop a novel temporal complex network approach to quantify the US county level spread dynamics of COVID-19. The objective is to study the effects of the local spread dynamics, COVID-19 cases and death, and Google search activities on the US stock market. We use both conventional econometric and Machine Learning (ML) models. The results suggest that COVID-19 cases and deaths, its local spread, and Google searches have impacts on abnormal stock prices between January 2020 to May 2020. In addition, incorporating information about local spread significantly improves the performance of forecasting models of the abnormal stock prices at longer forecasting horizons. On the other hand, although a few COVID-19 related variables, e.g., US total deaths and US new cases exhibit causal relationships on price volatility, COVID-19 cases and deaths, local spread of COVID-19, and Google search activities do not have impacts on price volatility.

In this paper we present a sequential hypothesis test for the detection of general jump size distrubution. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the crude oil data set, and the deterministic component is implemented to improve the Barndorff-Nielsen and Shephard model, a commonly used stochastic model for derivative and commodity market analysis.

We have proposed to develop a global hybrid deep learning framework to predict the daily prices in the stock market. With representation learning, we derived an embedding called Stock2Vec, which gives us insight for the relationship among different stocks, while the temporal convolutional layers are used for automatically capturing effective temporal patterns both within and across series. Evaluated on S&P 500, our hybrid framework integrates both advantages and achieves better performance on the stock price prediction task than several popular benchmarked models.

The world's stock markets display a strikingly suspicious pattern of overnight and intraday returns. Overnight returns to major stock market indices over the past few decades have been wildly positive, while intraday returns have been disturbingly negative. The cause of these astonishingly consistent return patterns is unknown. We highlight the features of these extraordinary patterns that have hindered the construction of any plausible innocuous explanation. We then use those same features to deduce the only plausible explanation so far advanced for these strikingly suspicious returns.

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial networks (GANs). We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy (MMD). We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data based examples for electricity demand profiles and day-ahead electricity prices.

In this paper we briefly review two recent use-cases of quantum optimization algorithms applied to hard problems in finance and economy. Specifically, we discuss the prediction of financial crashes as well as dynamic portfolio optimization. We comment on the different types of quantum strategies to carry on these optimizations, such as those based on quantum annealers, universal gate-based quantum processors, and quantum-inspired Tensor Networks.

This paper analyzes the differences in poverty in high wealth communities and low wealth communities. We first discuss methods of measuring poverty and analyze the causes of individual poverty and poverty in the Bay Area. Three cases are considered regarding relative poverty. The first two cases involve neighborhoods in the Bay Area while the third case evaluates two neighborhoods within the city of San Jose, CA. We find that low wealth communities have more crime, more teen births, and more cost-burdened renters because of high concentrations of temporary and seasonal workers, extensive regulations on greenhouse gas emissions, minimum wage laws, and limited housing supply. In the conclusion, we review past attempts to alleviate the effects of poverty and give suggestions on how future policy can be influenced to eventually create a future free of poverty.