We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on an multidimensional portfolio valuation problem.

The artificial segmentation of an investment management process into a workflow with silos of offline human operators can restrict silos from collectively and adaptively pursuing a unified optimal investment goal. To meet the investor's objectives, an online algorithm can provide an explicit incremental approach that makes sequential updates as data arrives at the process level. This is in stark contrast to offline (or batch) processes that are focused on making component level decisions prior to process level integration. Here we present and report results for an integrated, and online framework for algorithmic portfolio management. This article provides a workflow that can in-turn be embedded into a process level learning framework. The workflow can be enhanced to refine signal generation and asset-class evolution and definitions. Our results confirm that we can use our framework in conjunction with resampling methods to outperform naive market capitalisation benchmarks while making clear the extent of back-test over-fitting. We consider such an online update framework to be a crucial step towards developing intelligent portfolio selection algorithms that integrate financial theory, investor views, and data analysis with process-level learning.

SREC markets are a market-based system designed to incentivize solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a certificate for each MWh generated. Regulated firms seek to navigate the market to minimize the cost imposed on them, by modulating their SREC generation and trading activities. As such, the SREC market can be viewed through the lens of a large stochastic game with heterogeneous agents, where agents interact through the market price of the certificates. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Our market participants optimize costs accounting for trading frictions, cost of generation, SREC penalty, and generation uncertainty. Using techniques from variational analysis, we characterize firms' optimal controls as the solution of a new class of McKean-Vlasov FBSDE and determine the equilibrium SREC price. We further prove that MFG strategy has the $\epsilon$-Nash property for the finite player game. Finally, we numerically solve the MV-FBSDEs and conclude by demonstrating how firms behave in equilibrium using simulated examples.

This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window averaged sample estimate of the second order cumulant spectrum to build a test statistic with an asymptotic complex standard normal distribution. We derive the test statistic, study the properties of the test and demonstrate its application using 137Cs gamma ray decay data. Future areas of research include testing for strict stationarity of graph signals, with applications in learning convolutional neural networks on graphs, denoising, and inpainting.

The rank-size plots of very different systems are usually described in terms of Zipf's law, but the deep meaning of this scaling law is still controversial. We show how usual criteria used to identify Zipf's scaling fail to capture an essential feature of this phenomenon, that is the coherent evolution of the system and the space in which it is embedded. We therefore identify a Zipfian dynamics in terms of dynamical constraints which relate in time the level of sampling and the parameters of the probability distribution of sizes. This permits to introduce the concepts of coherent evolution, which is the key ingredient to develop a genuine Zipf's behaviour. We finally discuss a number of practical examples. For instance, earthquakes can evolve only incoherently and thus show only a spurious Zipf's law, while natural language dynamics is intrinsically Zipfian due to dynamical coherence imposed by grammar rules.

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation (PDE). We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation into two quasi one-dimensional equations with the variable on the other dimension fixed, which helps to lower the computational cost. Numerical results show that the iterative splitting method together with an artificial boundary condition (ABC) based on the method by Li and Huang (2019) gives the most accurate option price and Greeks compared to the classic finite difference method with the commonly-used boundary conditions in Heston (1993).

This paper is the first of a series of short articles that explore the efficiency of major cryptocurrency markets. A number of statistical tests and properties of statistical distributions will be used to assess if cryptocurrency markets are efficient, and how their efficiency changes over time. In this paper, we analyze autocorrelation of returns in major cryptocurrency markets using the following methods: Pearson's autocorrelation coefficient of different orders, Ljung-Box test, and first-order Pearson's autocorrelation coefficient in a rolling window. All experiments are conducted on the BTC/USD, ETH/USD, ETH/BTC markets on Bitfinex exchange, and the XBT/USD market on Bitmex exchange, each on 5-minute, 1-hour, 1-day, and 1-week time frames. The results are represented visually on charts. Statistically significant autocorrelation is persistently present on the 5m and 1H time frames on all markets. The tests disagree on the 1D and 1W time frames. The results of this article are fully reproducible. Used datasets, source code, and a runnable Jupyter Notebook are available on GitHub.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximisation. We propose a stylized model with a history-dependent utility function where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find in particular that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behaviour.

In this paper, we are interested to focus on the critical periods in the economy which are characterized by large fluctuations in macroeconomic indicators.

To capture unusual and large fluctuations of inflation and unemployment, we concentrate on the non-Gaussianity of their distributions.

To this aim, by using the coupled multifractal approach, we analyze US data for a period of 70 years from 1948 until 2018 and measure the non-Gausianity of the distributions. Then, we investigate how the non-Gaussianity of the variables affects the coupling structure of them. By applying the multifractal method, one can see that the non-Gaussianity depends on the scales. While the non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year and for longer periods tends to Gaussian behavior, the non-Gaussianities of inflation persist for all time scales. Also, it is observed that the coupling structure of these variables tends to a Gaussian behavior after $2$ years.

This paper provides the state of the art of data science in economics. Through a novel taxonomy of applications and methods advances in data science are investigated. The data science advances are investigated in three individual classes of deep learning models, ensemble models, and hybrid models. Application domains include stock market, marketing, E-commerce, corporate banking, and cryptocurrency. Prisma method, a systematic literature review methodology is used to ensure the quality of the survey. The findings revealed that the trends are on advancement of hybrid models as more than 51% of the reviewed articles applied hybrid model. On the other hand, it is found that based on the RMSE accuracy metric, hybrid models had higher prediction accuracy than other algorithms. While it is expected the trends go toward the advancements of deep learning models.

We consider a quasi-metric topological structure for the construction of a new reinforcement learning model in the framework of financial markets. It is based on a Lipschitz type extension of reward functions defined in metric spaces. Specifically, the McShane and Whitney extensions are considered for a reward function which is defined by the total evaluation of the benefits produced by the investment decision at a given time. We define the metric as a linear combination of a Euclidean distance and an angular metric component. All information about the evolution of the system from the beginning of the time interval is used to support the extension of the reward function, but in addition this data set is enriched by adding some artificially produced states. Thus, the main novelty of our method is the way we produce more states -- which we call "dreams" -- to enrich learning. Using some known states of the dynamical system that represents the evolution of the financial market, we use our technique to simulate new states by interpolating real states and introducing some random variables. These new states are used to feed a learning algorithm designed to improve the investment strategy by following a typical reinforcement learning scheme.

This paper presents a continuous-time model of intraday trading, pricing, and liquidity with dynamic TWAP and VWAP benchmarks. The model is solved in closed-form for the competitive equilibrium and also for non-price-taking equilibria. The intraday trajectories of TWAP trading targets cause predictable intraday patterns of price pressure, and randomness in VWAP target trajectories induces additional randomness in intraday price-pressure patterns. TWAP and VWAP trading both reduce market liquidity and increase price volatility relative to just terminal trading targets alone. The model is computationally tractable, which lets us provide a number of numerical illustrations.

Due to expensive infrastructure and the difficulties in storage, supply conditions of natural gas are different from those of other traditional energy sources like petroleum or coal. To overcome these challenges, supplier countries require take-or-pay agreements for requested natural gas quantities. These contracts have many pre-clauses; if they are not met due to low/high consumption or other external factors, buyers must completely fulfill them. A similar contract is then imposed on distributors and wholesale consumers. It is thus important for all parties to forecast their daily, monthly, and annual natural gas demand to minimize their risk. In this paper, a model consisting of a modulated expansion in Fourier series, supplemented by deviations from comfortable temperatures as a regressor is proposed for the forecast of monthly and weekly consumption over a one-year horizon. This model is supplemented by a day-ahead feedback mechanism for the forecast of daily consumption. The method is applied to the study of natural gas consumption for major residential areas in Turkey, on a yearly, monthly, weekly, and daily basis. It is shown that residential heating dominates winter consumption and masks all other variations. On the other hand, weekend and holiday effects are visible in summer consumption and provide an estimate for residential and industrial use. The advantage of the proposed method is the capability of long term projections and to outperform time series methods.

We study stochastic volatility models in which the volatility process is a function of a continuous fractional stochastic process, which is an integral transform of the solution of an SDE satisfying the Yamada-Watanabe condition. We establish a small-noise large deviation principle for the log-price, and, for a special case of our setup, obtain logarithmic call price asymptotics for large strikes.

We consider a semilinear equation linked to the finite horizon consumption - investment problem under the stochastic factor framework and we prove it admits a classical solution and provide all obligatory estimates to successfully apply a verification reasoning. The paper covers the standard time additive utility, as well as the recursive utility framework. We extend existing results by considering more general factor dynamics including a non-trivial diffusion part and a stochastic correlation between assets and factors. In addition, this is the first paper which compromises many other optimization problems in finance, for example those related to the indifference pricing or the quadratic hedging problem. The extension of the result to the stochastic differential utility and robust portfolio optimization is provided as well. The essence of our paper lays in using improved stochastic methods to prove gradient estimates for suitable HJB equations with restricted control space.

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm's perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy, and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm's generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments and conduct comparisons of the optimal strategy to other candidate strategies.

We consider the general class of spectrally positive L\'evy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study $\textit{periodic}$ dividend strategies whereby dividend decisions are made according to a separate arrival process.

In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic $(b_u,b_l)$ strategy is optimal when decision times arrive according to an independent Poisson process. Such a strategy leads to lump sum dividends that bring the surplus back to $b_l$ as long as it is no less than $b_u$ at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.

We develop a model of electoral accountability with mainstream and alternative media. In addition to regular high- and low-competence types, the incumbent may be an aspiring autocrat who controls the mainstream media and will subvert democracy if retained in office. A truthful alternative media can help voters identify and remove these subversive types while re-electing competent leaders. A malicious alternative media, in contrast, spreads false accusations about the incumbent and demotivates policy effort. If the alternative media is very likely be malicious and hence is unreliable, voters ignore it and use only the mainstream media to hold regular incumbents accountable, leaving aspiring autocrats to win re-election via propaganda that portrays them as effective policymakers. When the alternative media's reliability is intermediate, voters heed its warnings about subversive incumbents, but the prospect of being falsely accused demotivates effort by regular incumbents and electoral accountability breaks down.

We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst-case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model.

We characterize the minimal time horizon over which any market with $d \geq 2$ stocks and sufficient intrinsic volatility admits relative arbitrage. If $d \in \{2,3\}$, the minimal time horizon can be computed explicitly, its value being zero if $d=2$ and $\sqrt{3}/(2\pi)$ if $d=3$. If $d \geq 4$, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in $R^d$ that we call the minimum curvature flow.

We provide an analytically treatable model that describes in a unified manner income distribution for all income categories. The approach is based on a master equation with growth and reset terms. The model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the Cluj county (Romania). In agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters. The non-universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio-economic regulations.

A market consisting of a generator with thermal and renewable generation capability, a set of non-preemptive loads (i.e., loads which cannot be interrupted once started), and an independent system operator (ISO) is considered. Loads are characterized by durations, power demand rates and utility for receiving service, as well as disutility functions giving preferences for time slots in which service is preferred. Given this information, along with the generator's thermal generation cost function and forecast renewable generation, the social planner solves a mixed integer program to determine a load activation schedule which maximizes social welfare. Assuming price taking behavior, we develop a competitive equilibrium concept based on a relaxed version of the social planner's problem which includes prices for consumption and incentives for flexibility, and allows for probabilistic allocation of power to loads. Considering each load as representative of a population of identical loads with scaled characteristics, we demonstrate that the relaxed social planner's problem gives an exact solution to the original mixed integer problem in the large population limit, and give a market mechanism for implementing the competitive equilibrium.

In this paper we develop a semi-closed form solutions for the barrier (perhaps, time-dependent) and American options written on the underlying stock which follows a time-dependent OU process with a log-normal drift. This model is equivalent to the familiar Hull-White model in FI, or a time dependent OU model in FX. Semi-closed form means that given the time-dependent interest rate, continuous dividend and volatility functions, one need to solve numerically a linear (for the barrier option) or nonlinear (for the American option) Fredholm equation of the first kind. After that the option prices in all cases are presented as one-dimensional integrals of combination of the above solutions and Jacobi theta functions. We also demonstrate that computationally our method is more efficient than the backward finite difference method used for solving these problems, and can also be as efficient as the forward finite difference solver while providing better accuracy and stability.

We investigate the computational issues related to the memory size in the estimation of quadratic covariation using financial ultra-high-frequency data. In the multivariate price process, we consider both contamination by the market microstructure noise and the non-synchronous observations. We express the multi-scale, flat-top realized kernel, non-flat-top realized kernel, pre-averaging and modulated realized covariance estimators in a quadratic form and fix their bandwidth parameter at a constant value. This allows us to operate with limited memory and formulate such estimation approach as a streaming algorithm. We compare the performance of the estimators with fixed bandwidth parameter in a simulation study. We find that the estimators ensuring positive semidefiniteness require much higher bandwidth than the estimators without such constraint.

Sustainable business models also offer banks competitive advantages such as increasing brand reputation and cost reduction. However, no framework is presented to evaluate the sustainability of banking business models. To bridge this theoretical gap, the current study using A Delphi-Analytic Hierarchy Process method, firstly, developed a sustainable business model to evaluate the sustainability of the business model of banks. In the second step, the sustainability performance of sixteen banks from eight European countries including Norway, the UK, Poland, Hungary, Germany, France, Spain, and Italy, assessed. The proposed business model components of this study were ranked in terms of their impact on achieving sustainability goals. Consequently, the proposed model components of this study, based on their impact on sustainability, are respectively value proposition, core competencies, financial aspects, business processes, target customers, resources, technology, customer interface, and partner network. The results of the comparison of the banks studied by each country disclosed that the sustainability of the Norwegian and German banks business models is higher than in other counties. The studied banks of Hungary and Spain came in second, the banks of the UK, Poland, and France ranked third, and finally, the Italian banks ranked fourth in the sustainability of their business models.

In order to face the expected increasing demand of energy crops without creating conflicts of land occupation sustainability, farmers need to find reliable alternatives in marginal agricultural areas where the production of food hardly ever is economically and environmentally sustainable. The purpose of this work was the study of the viability of the introduction of new non food crops in marginal areas of real farms. This study compares the profit margin and the energy and environmental performance of growing tall wheatgrass, in the marginal area of a rainfed farm versus rye, the annual crop sowed traditionally in the marginal area of the farm. The cited farm owned 300 ha of which about 13 percent was marginal. The methodology was based on the use of the profit margin of the crops as indicator for the economic assessment and Life Cycle Assessment LCA as technique for the energy and the environmental evaluations. Results of the economic analysis showed a slight enhancement of the profit margin for tall wheatgrass 156 Euro ha-1 y-1 compared to rye 145 Euro ha-1 y-1. Environmental LCA was driven by CO2 fixation due to soil organic matter increase and reduced inputs consumption for tall wheatgrass that produced a Global Warming Potential GWP of -1.9 Mg CO2 eq ha-1 y-1 versus 1.6 Mg CO2 eq ha-1 y-1 obtained for rye. Tall wheatgrass cultivation primary energy consumption was less than 40 percent of rye s consumption. According to the results achieved it was concluded that tall wheatgrass is better option than rye from the energy and the environmental point of views and slight better option from the economic view. Considering these results, monetarization of the CO2 eq reductions of tall wheatgrass compared to rye is essential to improve its profit margin and promote the implantation of this new crop in marginal areas of farms.

While the coronavirus spreads around the world, governments are attempting to reduce contagion rates at the expense of negative economic effects. Market expectations have plummeted, foreshadowing the risk of a global economic crisis and mass unemployment. Governments provide huge financial aid programmes to mitigate the expected economic shocks. To achieve higher effectiveness with cyclical and fiscal policy measures, it is key to identify the industries that are most in need of support. In this study, we introduce a data-mining approach to measure the industry-specific risks related to COVID-19. We examine company risk reports filed to the U.S. Securities and Exchange Commission (SEC). This data set allows for a real-time analysis of risk assessments. Preliminary findings suggest that the companies' awareness towards corona-related business risks is ahead of the overall stock market developments by weeks. The risk reports differ substantially between industries, both in magnitude and in nature. Based on natural language processing techniques, we can identify corona-related risk topics and their perceived relevance for different industries. Our approach allows to distinguish the industries by their reported risk awareness towards COVID-19. The preliminary findings are summarised an online index. The CoRisk-Index tracks the industry-specific risk assessments related to the crisis, as it spreads through the economy. The tracking tool could provide relevant empirical data to inform models on the immediate economic effects of the crisis. Such complementary empirical information could help policy-makers to effectively target financial support and to mitigate the economic shocks of the current crisis.

Over the past decade, millions of companies have filed for bankruptcy. This has been caused by a plethora of reasons, namely, high interest rates, heavy debts and government regulations. The effect of a company going bankrupt can be devastating, hurting not only workers and shareholders, but also clients, suppliers and any related external companies. One of the aims of this paper is to provide a framework for company bankruptcy to be predicted by making use of financial figures, provided by our external dataset, in conjunction with the sentiment of news articles about certain sectors. News articles are used to attempt to quantify the sentiment on a company and its sector from an external perspective, rather than simply using internal figures. This work builds on previous studies carried out by multiple researchers, to bring us closer to lessening the impact of such events.