We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown, in the accompanying paper (Fujii-Takahashi (2020)), that the solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit. In this work, we prove the existence of a unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the strong convergence to the corresponding mean-field limit under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit.

We review the state of the art of clustering financial time series and the study of their correlations alongside other interaction networks. The aim of this review is to gather in one place the relevant material from different fields, e.g. machine learning, information geometry, econophysics, statistical physics, econometrics, behavioral finance. We hope it will help researchers to use more effectively this alternative modeling of the financial time series. Decision makers and quantitative researchers may also be able to leverage its insights. Finally, we also hope that this review will form the basis of an open toolbox to study correlations, hierarchies, networks and clustering in financial markets.

We introduce a simple model for equity index derivatives. The model generalizes well known L\`evy Normal Tempered Stable processes (e.g. NIG and VG) with time dependent parameters. It accurately fits Equity index implied volatility surfaces in the whole time range of quoted instruments, including small time horizon (few days) and long time horizon options (years). We prove that the model is an Additive process that is constructed using an Additive subordinator. This allows us to use classical L\`evy-type pricing techniques. We discuss the calibration issues in detail and we show that, in terms of mean squared error, calibration is on average two orders of magnitude better than both L\`evy processes and Self-similar alternatives. We show that even if the model loses the classical stationarity property of L\`evy processes, it presents interesting scaling properties for the calibrated parameters.

Recently, most stock exchanges in the U.S. employ maker-taker fees, in which an exchange pays rebates to traders placing orders in the order book and charges fees to traders taking orders from the order book. Maker-taker fees encourage traders to place many orders that provide market liquidity to the exchange. However, it is not clear how maker-taker fees affect the total cost of a taking order, including all the charged fees and the market impact. In this study, we investigated the effect of maker-taker fees on the total cost of a taking order with our artificial market model, which is an agent-based model for financial markets. We found that maker-taker fees encourage market efficiency but increase the total costs of taking orders.

This thesis serves three primary purposes, first of which is to forecast two stocks, i.e. Goldman Sachs (GS) and General Electric (GE). In order to forecast stock prices, we used a long short-term memory (LSTM) model in which we inputted the prices of two other stocks that lie in rather close correlation with GS. Other models such as ARIMA were used as benchmark. Empirical results manifest the practical challenges when using LSTM for forecasting stocks. One of the main upheavals was a recurring lag which we called "forecasting lag".

The second purpose is to develop a more general and objective perspective on the task of time series forecasting so that it could be applied to assist in an arbitrary that of forecasting by ANNs. Thus, attempts are made for distinguishing previous works by certain criteria (introduced by a review paper written by Ahmed Tealab) so as to summarise those including effective information. The summarised information is then unified and expressed through a common terminology that can be applied to different steps of a time series forecasting task.

The last but not least purpose of this thesis is to elaborate on a mathematical framework on which ANNs are based. We are going to use the framework introduced in the book "Neural Networks in Mathematical Framework" by Anthony L. Caterini in which the structure of a generic neural network is introduced and the gradient descent algorithm (which incorporates backpropagation) is introduced in terms of their described framework. In the end, we use this framework for a specific architecture, which is recurrent neural networks on which we concentrated and our implementations are based. The book proves its theorems mostly for classification case. Instead, we proved theorems for regression case, which is the case of our problem.

While researchers in the asset management industry have mostly focused on techniques based on financial and risk planning techniques like Markowitz efficient frontier, minimum variance, maximum diversification or equal risk parity, in parallel, another community in machine learning has started working on reinforcement learning and more particularly deep reinforcement learning to solve other decision making problems for challenging task like autonomous driving, robot learning, and on a more conceptual side games solving like Go. This paper aims to bridge the gap between these two approaches by showing Deep Reinforcement Learning (DRL) techniques can shed new lights on portfolio allocation thanks to a more general optimization setting that casts portfolio allocation as an optimal control problem that is not just a one-step optimization, but rather a continuous control optimization with a delayed reward. The advantages are numerous: (i) DRL maps directly market conditions to actions by design and hence should adapt to changing environment, (ii) DRL does not rely on any traditional financial risk assumptions like that risk is represented by variance, (iii) DRL can incorporate additional data and be a multi inputs method as opposed to more traditional optimization methods. We present on an experiment some encouraging results using convolution networks.

The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution remains a challenge. In the presence of high-dimensionality in the data, the sample covariance estimator becomes ill-conditioned and leads to suboptimal portfolios out-of-sample. To address this issue, we review recently proposed efficient estimation methods for the covariance matrix and extend the literature by suggesting a multi-fold cross-validation technique for selecting the necessary tuning parameters within each method. Conducting an extensive empirical analysis with four datasets based on the S&P 500, we show that the data-driven choice of specific tuning parameters with the proposed cross-validation improves the out-of-sample performance of the global minimum-variance portfolio. In addition, we identify estimators that are strongly influenced by the choice of the tuning parameter and detect a clear relationship between the selection criterion within the cross-validation and the evaluated performance measure.

We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals used to capture the non-Gaussian cryptocurrency return dynamics. Based on the time series model, we optimize the portfolio in terms of Foster-Hart risk. Those sophisticated techniques are not yet documented in the context of cryptocurrency. Statistical tests suggest that the MNTS distributed GARCH model fits better with cryptocurrency returns than the competing GARCH-type models. We find that Foster-Hart optimization yields a more profitable portfolio with better risk-return balance than the prevailing approach.

Probabilistic forecasting of power consumption in a middle-term horizon (months to a year) is a main challenge in the energy sector. It plays a key role in planning future generation plants and transmission grid. We propose a new model that incorporates trend and seasonality features as in traditional time-series analysis and weather conditions as explicative variables in a parsimonious machine learning approach, known as Gaussian Process. Applying to a daily power consumption dataset in North East England provided by one of the largest energy suppliers, we obtain promising results in Out-of-Sample density forecasts up to one year, even using a small dataset, with only a two-year In-Sample data. In order to verify the quality of the achieved power consumption probabilistic forecast we consider measures that are common in the energy sector as pinball loss and Winkler score and backtesting conditional and unconditional tests, standard in the banking sector after the introduction of Basel II Accords.

The present work addresses theoretical and practical questions in the domain of Deep Learning for High Frequency Trading. State-of-the-art models such as Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are reviewed and compared on the same tasks, feature space and dataset, and then clustered according to pairwise similarity and performance metrics. The underlying dimensions of the modeling techniques are hence investigated to understand whether these are intrinsic to the Limit Order Book's dynamics. We observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.

This article presents the results of a cluster analysis of the regions of the Russian Federation in terms of the main parameters of socio-economic development according to the data presented in the official data sources of the Federal State Statistics Service (Rosstat). Studied and analyzed the domestic and foreign (Eurostat) methodology for assessing the socio-economic development of territories. The aim of the study is to determine the main parameters of territorial differentiation and to identify key indicators that affect the socio-economic development of Russian regions. The authors have carried out a classification of the constituent entities of the Russian Federation not in terms of territorial location and geographical features, but in terms of the specifics and key parameters of the socio-economic situation.

We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity with decreasing volatility error. Forecasts are prone to idiosyncratic noise as well as common noise (weather). Agents production capacities are subject to independent random outages, which are each modelled by a Markov chain. The equilibrium price is defined as the price that minimises trading cost plus imbalance cost of each agent and satisfies the usual market clearing condition. Existence and uniqueness of the equilibrium are proved, and we show that the equilibrium price and the optimal trading strategies are martingales. The main economic insights are the following. (i) When there is no uncertainty on generation, it is shown that the market price is a convex combination of forecasted marginal cost of each agent, with deterministic weights. Furthermore, the equilibrium market price follows Almgren and Chriss's model and we identify the fundamental part as well as the permanent market impact. It turns out that heterogeneity across agents is a necessary condition for the Samuelson's effect to hold. (ii) When there is production uncertainty, the price volatility becomes stochastic but converges to the case without production uncertainty when the number of agents increases to infinity. Further, on a two-agent case, we show that the potential outages of a low marginal cost producer reduces her sales position.

In nature and human societies, the effects of homogeneous and heterogeneous characteristics on the evolution of collective behaviors are quite different from each other. It is of great importance to understand the underlying mechanisms of the occurrence of such differences. By incorporating pair pattern strategies and reference point strategies into an agent-based model, we have investigated the coupled effects of heterogeneous investment strategies and heterogeneous risk tolerance on price fluctuations. In the market flooded with the investors with homogeneous investment strategies or homogeneous risk tolerance, large price fluctuations are easy to occur. In the market flooded with the investors with heterogeneous investment strategies or heterogeneous risk tolerance, the price fluctuations are suppressed. For a heterogeneous population, the coexistence of investors with pair pattern strategies and reference point strategies causes the price to have a slow fluctuation around a typical equilibrium point and both a large price fluctuation and a no-trading state are avoided, in which the pair pattern strategies push the system far away from the equilibrium while the reference point strategies pull the system back to the equilibrium. A theoretical analysis indicates that the evolutionary dynamics in the present model is governed by the competition between different strategies. The strategy that causes large price fluctuations loses more while the strategy that pulls the system back to the equilibrium gains more. Overfrequent trading does harm to one's pursuit for more wealth.

Extensive research has established a strong influence of product display on demand. In this domain, managers have many tools at their disposal to influence the demand through the product display, like assortment,shelf-space or allocating profitable products to highly attractive shelf locations. In this research, we focus on the influence of the product arrangement on competition among products within the display. Intuitively,products located next to each other are compared more often than when they are placed far apart. We introduce a model that allows product competition effects mediated by their relative position in the display. This model naturally produces an increased competition on products located closer together, inducing demand correlations based on products proximity with their competitors in the shelf, and not only their relative characteristics. We fit this model to experimental data from physical retail stores and in online product displays.The proposed model shows this effect to be significant; moreover, this model outperforms traditional models in fit and prediction power, and shows that ignoring the shelf-implied competition generates a bias in the price sensitivity, affecting price and promotion strategies. The proposed model was used to evaluate different shelf displays, and to evaluate and select displays with higher profitability, by exploiting the influence on competition among products to shift demand to higher profitability products. Finally, from the model,we generate recommendations for retail managers to construct better shelf designs;testing these suggestions on our fitted model on retail store data, we achieve a 3% increase in profits over current shelf designs.

Information coefficient (IC) is a widely used metric for measuring investment managers' skills in selecting stocks. However, its adequacy and effectiveness for evaluating stock selection models has not been clearly understood, as IC from a realistic stock selection model can hardly be materially different from zero and is often accompanies with high volatility. In this paper, we investigate the behavior of IC as a performance measure of stick selection models. Through simulation and simple statistical modeling, we examine the IC behavior both statically and dynamically. The examination helps us propose two practical procedures that one may use for IC-based ongoing performance monitoring of stock selection models.

In 2012, SEC mandated all corporate filings for any company doing business in US be entered into the Electronic Data Gathering, Analysis, and Retrieval (EDGAR) system. In this work we are investigating ways to analyze the data available through EDGAR database. This may serve portfolio managers (pension funds, mutual funds, insurance, hedge funds) to get automated insights into companies they invest in, to better manage their portfolios. The analysis is based on Artificial Neural Networks applied to the data.} In particular, one of the most popular machine learning methods, the Convolutional Neural Network (CNN) architecture, originally developed to interpret and classify images, is now being used to interpret financial data. This work investigates the best way to input data collected from the SEC filings into a CNN architecture. We incorporate accounting principles and mathematical methods into the design of three image encoding methods. Specifically, two methods are derived from accounting principles (Sequential Arrangement, Category Chunk Arrangement) and one is using a purely mathematical technique (Hilbert Vector Arrangement). In this work we analyze fundamental financial data as well as financial ratio data and study companies from the financial, healthcare and IT sectors in the United States. We find that using imaging techniques to input data for CNN works better for financial ratio data but is not significantly better than simply using the 1D input directly for fundamental data. We do not find the Hilbert Vector Arrangement technique to be significantly better than other imaging techniques.

Savage (1972) lays down the foundation of Bayesian decision theory, but asserts that it is not applicable in big worlds where the environment is complex. Using the theory of finite automaton to model belief formation, this paper studies the characteristics of optimal learning behavior in small and big worlds, where the complexity of the environment is low and high, respectively, relative to the cognitive ability of the decision maker. Confirming Savage's claim, optimal learning behavior is closed to Bayesian in small worlds but significantly different in big worlds. In addition, I show that in big worlds, the optimal learning behavior could exhibit a wide range of well-documented non-Bayesian learning behavior, including the use of heuristic, correlation neglect, persistent over-confidence, inattentive learning, and other behaviors of model simplification or misspecification. These results establish a clear and testable relationship between the prominence of non-Bayesian learning behavior, complexity and cognitive ability.

The trustless nature of permissionless blockchains renders overcollateralization a key safety component relied upon by decentralized finance (DeFi) protocols. Nonetheless, factors such as price volatility may undermine this mechanism. In order to protect protocols from suffering losses, undercollateralized positions can be \textit{liquidated}. In this paper, we present the first in-depth empirical analysis of liquidations on protocols for loanable funds (PLFs). We examine Compound, one of the most widely used PLFs, for a period starting from its conception to September 2020. We analyze participants' behavior and risk-appetite in particular, to elucidate recent developments in the dynamics of the protocol. Furthermore, we assess how this has changed with a modification in Compound's incentive structure and show that variations of only 3% in an asset's price can result in over 10m USD becoming liquidable. To further understand the implications of this, we investigate the efficiency of liquidators. We find that liquidators' efficiency has improved significantly over time, with currently over 70% of liquidable positions being immediately liquidated. Lastly, we provide a discussion on how a false sense of security fostered by a misconception of the stability of non-custodial stablecoins, increases the overall liquidation risk faced by Compound participants.

When stochastic control problems do not possess separability and/or monotonicity, the dynamic programming pioneered by Bellman in 1950s fails to work as a time-decomposition solution method. Such cases have posted a great challenge to the control society in both theoretical foundation and solution methodologies for many years. With the help of the progressive hedging algorithm proposed by Rockafellar and Wets in 1991, we develop a novel scenario-decomposition solution framework for stochastic control problems which could be nonseparable and/or non-monotonic, thus extending the reach of stochastic optimal control. We discuss then some of its promising applications, including online quadratic programming problems and dynamic portfolio selection problems with smoothing properties.

Two decades of studies have found significant regional differences in the timing of transitions in national business cycles and their durations. Earlier studies detect regional synchronization during business cycle expansions and contractions in Europe (Grayer, 2007), the U.S. (Hamilton and Owyang, 2012; Chung, 2016), and Japan (Wall, 2007). We investigate those findings more comprehensively for Japan. We draw upon business cycle data spanning 1978-2018 for all 47 Japanese prefectures and measure synchronization between them using a method prominent in nonlinear sciences but infrequently applied in business cycle studies. Our findings confirm that synchronization in Japan's prefectural business cycles increased during contractions and decreased during expansions throughout the period studied.

We find UK 'local lockdowns' of cities and small regions, focused on limiting how many people a household can interact with and in what settings, are effective in turning the tide on rising positive COVID-19 cases. Yet, by focusing on household mixing within the home, these local lockdowns have not inflicted the large declines in consumption accompanying the March 2020 national lockdown, which limited all social contact. Our study harnesses a new source of real-time, transaction-level consumption data that we show to be highly correlated with official statistics. The effectiveness of local lockdowns are evaluated applying a difference-in-difference approach which exploits nearby localities not subject to local lockdowns as comparison groups. Our findings indicate that policymakers may be able to contain virus outbreaks $\textit{without}$ killing local economies. However, the ultimate effectiveness of local lockdowns is expected to be highly dependent on co-ordination between regions and an effective system of testing.

Integrated Assessment Models (IAMs) of the climate and economy aim to analyze the impact and efficacy of policies that aim to control climate change, such as carbon taxes and subsidies. A major characteristic of IAMs is that their geophysical sector determines the mean surface temperature increase over the preindustrial level, which in turn determines the damage function. Most of the existing IAMs are perfect-foresight forward-looking models, assuming that we know all of the future information. However, there are significant uncertainties in the climate and economic system, including parameter uncertainty, model uncertainty, climate tipping risks, economic risks, and ambiguity. For example, climate damages are uncertain: some researchers assume that climate damages are proportional to instantaneous output, while others assume that climate damages have a more persistent impact on economic growth. Climate tipping risks represent (nearly) irreversible climate events that may lead to significant changes in the climate system, such as the Greenland ice sheet collapse, while the conditions, probability of tipping, duration, and associated damage are also uncertain. Technological progress in carbon capture and storage, adaptation, renewable energy, and energy efficiency are uncertain too. In the face of these uncertainties, policymakers have to provide a decision that considers important factors such as risk aversion, inequality aversion, and sustainability of the economy and ecosystem. Solving this problem may require richer and more realistic models than standard IAMs, and advanced computational methods. The recent literature has shown that these uncertainties can be incorporated into IAMs and may change optimal climate policies significantly.

The sub-fractional Brownian motion is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the fractional Brownian motion (fBm). The mixed process, a linear combination between a Bm and an independent sfBm, called mixed sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding the semi-martingale property for H>3/4, is a suitable candidate to use in price fluctuation modeling, in particular for option pricing. In this note, we arrive at the European Call price under the consider the Constant Elasticity of Variance (CEV) model driven by a mixed sub-fractional Brownian motion.

The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology involves the degree of multiscaling at a particular time instance, the multiscaling trend which is calculated by the Change-Point Analysis method, and a rigorous evaluation of the statistical significance of the results. Using this algorithm, we have identified particular patterns in the temporal co-evolution of the different $H_q$ time-series. These GHE patterns, distinguish in a statistically robust way, not only between time periods of uniscaling and multiscaling, but also among different types of multiscaling: symmetric multiscaling (M) and asymmetric multiscaling (A). We apply the visual methodology to time-series comprising of daily close prices of four stock market indices: two major ones (S\&P~500 and NIKKEI) and two peripheral ones (Athens Stock Exchange general Index and Bombay-SENSEX). Results show that multiscaling varies greatly with time: time periods of strong multiscaling behavior and time periods of uniscaling behavior are interchanged while transitions from uniscaling to multiscaling behavior occur before critical market events, such as stock market bubbles. Moreover, particular asymmetric multiscaling patterns appear during critical stock market eras and provide useful information about market conditions. In particular, they can be used as 'fingerprints' of a turbulent market period as well as provide warning signals for an upcoming stock market 'bubble'. The applied visual methodology also appears to distinguish between exogenous and endogenous stock market crises, based on the observed patterns before the actual events.

In recent years, machine learning has become prevalent in numerous tasks, including algorithmic trading. Stock market traders utilize learning models to predict the market's behavior and execute an investment strategy accordingly. However, learning models have been shown to be susceptible to input manipulations called adversarial examples. Yet, the trading domain remains largely unexplored in the context of adversarial learning. This is mainly because of the rapid changes in the market which impair the attacker's ability to create a real-time attack. In this study, we present a realistic scenario in which an attacker gains control of an algorithmic trading bots by manipulating the input data stream in real-time. The attacker creates an universal perturbation that is agnostic to the target model and time of use, while also remaining imperceptible. We evaluate our attack on a real-world market data stream and target three different trading architectures. We show that our perturbation can fool the model at future unseen data points, in both white-box and black-box settings. We believe these findings should serve as an alert to the finance community about the threats in this area and prompt further research on the risks associated with using automated learning models in the finance domain.