Econophysics & Complex Systems

This work analyzes data on all public US firms in the 50 year period 1970-2019, and presents 18 stylized facts of their scale, income, growth, return, investment, and dynamism. Special attention is given to (i) identifying distributional forms; and (ii) scale effects – systematic difference between

We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary relational system without assumed metric, temporal, or price coord

Classical correlation and rolling PCA summarize market dependence through covariance spectra, but they do not provide a unified operator representation for entropy, purity-based mixing, and standardized structural deviations built from rolling multi-feature trajectories. We propose the Quantum Netwo

We propose a novel model, the Hyped Log-Periodic Power Law Model (HLPPL), to the problem of quantifying and detecting financial bubbles, an ever-fascinating one for academics and practitioners alike. Bubble labels are generated using a Log-Periodic Power Law (LPPL) model, sentiment scores, and a hyp

As global financial markets become increasingly interconnected, financial contagion has developed into a major influencer of asset price dynamics. Motivated by this context, our study explores financial contagion both within and between asset communities. We contribute to the literature by examining

We introduce a novel rough Bergomi (rBergomi) model featuring a variance-driven exponentially weighted moving average (EWMA) time-dependent Hurst parameter $H_t$, fundamentally distinct from recent machine learning and wavelet-based approaches in the literature. Our framework pioneers a unified roug

This paper introduces a novel framework for analyzing systemic risk in financial markets through multi-scale network dynamics using Model Context Protocol (MCP) for agent communication. We develop an integrated approach that combines transfer entropy networks, agent-based modeling, and wavelet decom

We study decades-long historic distributions of accumulated S&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets – Black Monday, Tech Bubble, Financial Crisis and Covid Pandemic – which are reflected in the tail ends

Traders on financial markets generate non-Markovian effects in various ways, particularly through their competition with one another which can be interpreted as a game between different (types of) traders. To quantify the market mechanisms, we empirically analyze self-response functions for pairs of

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an

Volatility, as a measure of uncertainty, plays a crucial role in numerous financial activities such as risk management. The Econometrics and Machine Learning communities have developed two distinct approaches for financial volatility forecasting: the stochastic approach and the neural network (NN) a

This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided

This paper is concerned with upstreamness and downstreamness of industries and countries. Upstreamness and downstreamness measure respectively the average distance of an industrial sector from final consumption and from primary inputs. Recently, Antràs and Chor reported a puzzling and counter-intuit

We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. [2020]. The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed versio

Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mike-Farmer (LMF) order-splitting theory. However, quantitative tests of this theory have historically

Financial markets are complex adaptive systems characterized by collective behavior and abrupt regime shifts, particularly during crises. This paper studies time-varying dependencies in Nordic equity markets and examines whether correlation-eigenstructure dynamics can be exploited for regime-aware p

We propose a general CoVaR framework that extends the traditional CoVaR by incorporating diverse expert views and information, such as asset moment characteristics, quantile insights, and perspectives on the relative loss distribution between two assets. To integrate these expert views effectively w

This paper presents an in-depth analysis of stylized facts in the context of futures on German bonds. The study examines four futures contracts on German bonds: Schatz, Bobl, Bund and Buxl, using tick-by-tick limit order book datasets. It uncovers a range of stylized facts and empirical observations

For a sequence of binary bets, the Kelly criterion provides a closed-form solution that maximizes the expected growth rate of wealth. In contrast, when multiple bets are placed simultaneously (e.g., in portfolio allocation or prediction markets), the optimal Kelly strategy generally requires numeric

Time series encountered in practice are rarely stationary. When the data distribution changes, a forecasting model trained on past observations can lose accuracy. We study a small-footprint test-time adaptation (TTA) framework for causal timeseries forecasting and direction classification. The backb

Evaluating faithfulness of Large Language Models (LLMs) to a given task is a complex challenge. We propose two new unsupervised metrics for faithfulness evaluation using insights from information theory and thermodynamics. Our approach treats an LLM as a bipartite information engine where hidden lay

Decentralized Exchanges (DEXs) are now a significant component of the financial world where billions of dollars are traded daily. Differently from traditional markets, which are typically based on Limit Order Books, DEXs typically work as Automated Market Makers, and, since the implementation of Uni

Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interp

This study presents a comprehensive empirical investigation of the presence of long-range dependence (LRD) in the dynamics of major U.S. stock market indexes–S&P 500, Dow Jones, and Nasdaq–at daily, weekly, and monthly frequencies. We employ three distinct methods: the classical rescaled range (R/S)

This study measures the long memory of investor-segregated cash flows within the Korean equity market from 2015 to 2024. Applying detrended fluctuation analysis (DFA) to BUY, SELL, and NET aggregates, we estimate the Hurst exponent ($H$) using both a static specification and a 250-day rolling window

This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the abs

Providing optimal portfolio selection for investors has always been one of the hot topics in academia. In view of the traditional portfolio model could not adapt to the actual capital market and can provide erroneous results. This paper innovatively constructs a mean-detrended cross-correlation port

Portfolio diversification, traditionally measured through asset correlations and volatilitybased metrics, is fundamental to managing financial risk. However, existing diversification metrics often overlook non-numerical relationships between assets that can impact portfolio stability, particularly d

Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with const

Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the “noise”. Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted as collective modes behavior while the modes under are usual

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $κ$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the $κ$-exponential function that is asymptotically exponential for small values and a

The correlation-based financial networks are studied intensively. However, previous studies ignored the importance of the anti-correlation. This paper is the first to consider the anti-correlation and positive correlation separately, and accordingly construct the weighted temporal anti-correlation a

We extend the opinion formation approach to probe the world influence of economical organizations. Our opinion formation model mimics a battle between currencies within the international trade network. Based on the United Nations Comtrade database, we construct the world trade network for the years

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper w

This paper adopts the random matrix theory (RMT) to analyze the correlation structure of the global agricultural futures market from 2000 to 2020. It is found that the distribution of correlation coefficients is asymmetric and right skewed, and many eigenvalues of the correlation matrix deviate from

The emergence of cryptoassets has sparked a paradigm shift in the world of finance and investment, ushering in a new era of digital assets with profound implications for the future of currency and asset management. A recent study showed that during the bubble period around the year, 2018, the price

Financial portfolio construction problems are often formulated as quadratic and discrete (combinatorial) optimization that belong to the nondeterministic polynomial time (NP)-hard class in computational complexity theory. Ising machines are hardware devices that work in quantum-mechanical/quantum-in

Modeling financial markets based on empirical data poses challenges in selecting the most appropriate models. Despite the abundance of empirical data available, researchers often face difficulties in identifying the best-fitting model. Long-range memory and self-similarity estimators, commonly used

This paper deals with tail diversification in financial time series through the concept of statistical independence by way of differential entropy and mutual information. By using moments as contrast functions to isolate the tails of the return distributions, we recover the tail covariance matrix, a

We organize existing empirical regularities of cryptocurrencies into seven stylized facts and analyze cryptocurrencies through the lens of empirical asset pricing. We find important similarities with traditional markets–risk-adjusted performance so far is broadly comparable, and the cross-section o

We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate th

We apply the concept of Rayleigh-Jeans thermalization of classical fields for a description of the world Gross Domestic Product (GDP) distribution over countries. The thermalization appears due to a variety of interactions between countries with conservation of two integrals being total GDP and prob

We compute exactly the overlap between the eigenvectors of two large empirical covariance matrices computed over intersecting time intervals, generalizing the results obtained previously for non-intersecting intervals. Our method relies on a particular form of Girko linearisation and extended local

We investigate the mechanisms behind the power-law distribution of stock returns using artificial market simulations. While traditional financial theory assumes Gaussian price fluctuations, empirical studies consistently show that the tails of return distributions follow a power law. Previous resear

In this paper, we introduce a parametrized family of prices derived from the Maximum Entropy Principle. The price is obtained from the distribution that minimizes bias, given the bid and ask volume imbalance at the top of the order book. Under specific parameter choices, it closely approximates the

We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal) as a compound of a large-scale multivariate distribution wi

This paper presents a comprehensive statistical analysis of the Web3 ecosystem, comparing various Web3 tokens with traditional financial assets across multiple time scales. We examine probability distributions, tail behaviors, and other key stylized facts of the returns for a diverse range of tokens

In this study, we developed a computational framework for simulating large-scale agent-based financial markets. Our platform supports trading multiple simultaneous assets and leverages distributed computing to scale the number and complexity of simulated agents. Heterogeneous agents make decisions i

The multifractal spectra of daily foreign exchange rates for US dollar (USD), the British Pound (GBP), the Euro (Euro) and the Japanese Yen (Yen) with respect to the Indian Rupee are analysed for the period 6th January 1999 to 24th July 2018. We observe that the time series of logarithmic returns of

We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by the order flow. The model features a concave transient impact

Using Malliavin calculus techniques, we obtain formulas for computing Greeks under different rough Volterra stochastic volatility models. Due to the fact that underlying prices are not always square integrable, we extend the classical integration by parts formula to integrable but not necessarily sq

We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invaria

In this work we address the question of the Multifractal detrended cross-correlation analysis method that has been subject to some controversies since its inception almost two decades ago. To this end we propose several new options to deal with negative cross-covariance among two time series, that m

This paper presents a method to identify causal interactions between two time series. The largest eigenvalue follows a Tracy-Widom distribution, derived from a Coulomb gas model. This defines causal interactions as the pushing and pulling of the gas, measurable by the variability of the largest eige

This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed

Agent-based models provide a constructive approach to studying emergent dynamics in life-like systems composed of interacting, adaptive agents. Financial markets serve as a canonical example of such systems, where collective price dynamics arise from individual decision-making. In this modeling trad

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing of switches and the selection of regimes through the genera

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant variables, especially in the presence of non-stationarity. We use a g

Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock return correlation matrix typically aligns with a rescaled

During his state visit to China in April 2023, Brazilian President Lula proposed the creation of a trade currency supported by the BRICS countries. Using the United Nations Comtrade database, providing the frame of the world trade network associated to 194 UN countries during the decade 2010 - 2020,

Selecting stock portfolios and assessing their relative volatility risk compared to the market as a whole, market indices, or other portfolios is of great importance to professional fund managers and individual investors alike. Our research uses the cross-sectional intrinsic entropy (CSIE) model to

We consider the dynamics and the interactions of multiple reinforcement learning optimal execution trading agents interacting with a reactive Agent-Based Model (ABM) of a financial market in event time. The model represents a market ecology with 3-trophic levels represented by: optimal execution lea

Generative models for financial time series often create data that look realistic and even reproduce stylized facts such as fat tails or volatility clustering. However, these apparent successes break down under trading backtests: models like GANs or WGAN-GP frequently collapse, yielding extreme and

Our research investigates the relationship between eco-innovation and earnings management among 567 firms listed on the FTSE All-Share Index from 2014 to 2022. By examining how sustainability-driven innovation influences financial reporting practices, we explore the strategic motivations behind inco

In the financial sector, a sophisticated financial time series simulator is essential for evaluating financial products and investment strategies. Traditional back-testing methods have mainly relied on historical data-driven approaches or mathematical model-driven approaches, such as various stochas

A cryptocurrency is a digital asset maintained by a decentralised system using cryptography. Investors in this emerging digital market are exploring the profitability potential of portfolios in place of single coins. Portfolios are particularly useful given that price forecasting in such a volatile

This paper investigates the evolving link between cryptocurrency and equity markets in the context of the recent wave of corporate Bitcoin (BTC) treasury strategies. We assemble a dataset of 39 publicly listed firms holding BTC, from their first acquisition through April 2025. Using daily logarithmi

To quantify the changes in the credit rating of a bond is an important mathematical problem for the credit rating industry. To think of the credit rating as the state a Markov chain is an interesting proposal leading to challenges in mathematical modeling. Since cumulative default rates are more rea

We study the problem of choosing the copula when the marginal distributions of a random vector are not all continuous. Inspired by four motivating examples including simulation from copulas, stress scenarios, co-risk measures, and dependence measures, we propose to use the checkerboard copula, that

This paper explores the application of Sample Entropy (SampEn) as a sophisticated tool for quantifying and predicting volatility in international oil price returns. SampEn, known for its ability to capture underlying patterns and predict periods of heightened volatility, is compared with traditional

Grains account for more than 50% of the calories consumed by people worldwide, and military conflicts, pandemics, climate change, and soaring grain prices all have vital impacts on food security. However, the complex price behavior of the global grain spot markets has not been well understood. A rec

In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to

We propose a virtual bidding strategy by modeling the price differences between the day-ahead market and the real-time market as Brownian motion with drift, where the drift rate and volatility are functions of meteorological variables. We then transform the virtual bidding problem into a mean-varian

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker’s control is represented by the probability of stopping within a given time-

We focus on large blackouts in electric distribution systems caused by extreme winds. Such events have a large cost and impact on customers. To quantify resilience to these events, we formulate large event risk and show how to calculate it from the historical outage data routinely collected by utili

This study examines the effects of Trump-era tariffs on financial market efficiency by applying multifractal detrended fluctuation analysis to the return and absolute return time series of six major financial assets: the S&P 500, SSEC, VIX, BTC/USD, EUR/USD, and Gold. Using the Hurst exponent $h(2)

Prediction markets mobilize financial incentives to forecast binary event outcomes through the aggregation of dispersed beliefs and heterogeneous information. Their growing popularity and demonstrated predictive accuracy in political elections have raised speculation and concern regarding their susc

Directional-change Intrinsic Time analysis has long revealed scaling laws in market microstructure, but the origin of their stability remains elusive. This article presents evidence that Intrinsic Time can be modeled as a memoryless exponential hazard process. Empirically, the proportion of directio

Through its initiative known as the Climate Change Act (2008), the Government of the United Kingdom encourages corporations to enhance their environmental performance with the significant aim of reducing targeted greenhouse gas emissions by the year 2050. Previous research has predominantly assessed

A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset’s price under this measure. But if t

This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes process. In this model we confirm the super-normal transition when

In this paper we analyze how market prices change in response to information processing among the market participants and how non-linear information dynamics drive market price movement. We analyze historical data of the SP 500 market for the period 1950 -2025 using the logistic Continuous Wavelet T

This study examines the impact of the coronavirus disease 2019 (COVID-19) pandemic on market efficiency by analyzing three time series – price returns, absolute returns, and volatility increments – in stock (Deutscher Aktienindex, Nikkei 225, Shanghai Stock Exchange (SSE), and Volatility Index) and

In financial market microstructure, there are two enigmatic empirical laws: (i) the market-order flow has predictable persistence due to metaorder splitters by institutional investors, well formulated as the Lillo-Mike-Farmer model. However, this phenomenon seems paradoxical given the diffusive and

In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling constraints and borrowing prohibition. The optimal feedback

Despite its practical significance, generating realistic synthetic financial time series is challenging due to statistical properties known as stylized facts, such as fat tails, volatility clustering, and seasonality patterns. Various generative models, including generative adversarial networks (GAN

We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to capture the exploration–exploitation balance essential for RL. U

Marketing is the way we ensure our sales are the best in the market, our prices the most accessible, and our clients satisfied, thus ensuring our brand has the widest distribution. This requires sophisticated and advanced understanding of the whole related network. Indeed, marketing data may exist i

An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equ

We present our Agent-Based Market Microstructure Simulation (ABMMS), an Agent-Based Financial Market (ABFM) that captures much of the complexity present in the US National Market System for equities (NMS). Agent-Based models are a natural choice for understanding financial markets. Financial markets

The first 100 days of Donald Trump second presidential term (January 20th - April 30th, 2025) featured policy actions with potential market repercussions, constituting a well-suited case study of a concentrated policy scenario. Here, we provide a first look at this period, rooted in the information

We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture volatility asymmetry. Our results show that QCL-based volatility pr

Through a novel approach, this paper shows that substantial change in stock market behavior has a statistically and economically significant impact on equity risk premium predictability both on in-sample and out-of-sample cases. In line with Auer’s ‘‘Bullish ratio’’, a ‘‘Bullish index’’ is introduce

Traditional art pricing models often lack fine measurements of painting content. This paper proposes a new content measurement: the Shannon information quantity measured by the singular value decomposition (SVD) entropy of the painting image. Using a large sample of artworks’ auction records and ima

Investor sentiment reflects the collective attitude of investors towards the asset, whether positive, negative or neutral. Market information, such as news and relevant social media posts, plays a significant role in shaping investor sentiment, which influences investment decisions accordingly. The

We employed Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) to investigate the complexity of Bitcoin, GBP/USD, gold, and natural gas price log-return time series. This study provides a comparative analysis of these markets and offers insig

This paper explores the mechanisms behind extreme financial events, specifically market crashes, by employing the theoretical framework of phase transitions. We focus on endogenous crashes, driven by internal market dynamics, and model these events as first-order phase transitions critical, stochast

Starting from a corpus of economic articles from The Wall Street Journal, we present a novel systematic way to analyse news content that evolves over time. We leverage on state-of-the-art natural language processing techniques (i.e. GPT3.5) to extract the most important entities of each article avai

Starting from the Pearson Correlation Matrix of stock returns and from the desire to obtain a reduced number of parameters relevant for the dynamics of a financial market, we propose to take the idea of a sectorial matrix, which would have a large number of parameters, to the reduced picture of a re

The covariance between the return of an asset and its realized volatility can be approximated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between