Econophysics & Complex Systems

This paper explores the bifurcative dynamics of an artificial stock market exchange (ASME) with endogenous, myopic traders interacting through a limit order book (LOB). We showed that agent-based price dynamics possess intrinsic bistability, which is not a result of randomness but an emergent proper

The basis of arbitrage methods depends on the circulation of information within the framework of the financial market. Following the work of Modigliani and Miller, it has become a vital part of discussions related to the study of financial networks and predictions. The emergence of the efficient mar

We study a martingale Schrödinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schrödinger potentials for this coupling. Namely, under certain conditions, the log-density of the optimal coupling is given b

In 1956 John Kelly wrote a paper at Bell Labs describing the relationship between gambling and Information Theory. What came to be known as the Kelly Criterion is both an objective and a closed-form solution to sizing wagers when odds and edge are known. Samuelson argued it was arbitrary and subject

As operators acting on the undetermined final settlement of a derivative security, expectation is linear but price is non-linear. When the market of underlying securities is incomplete, non-linearity emerges from the bid-offer around the mid price that accounts for the residual risks of the optimal

In this work, we study the effectiveness of employing archetypal aperiodic sequencing – namely Fibonacci, Thue-Morse, and Rudin-Shapiro – on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo’s Paradox with the Thue-Morse based strategy out

This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of macroeconomic variables have greater uncertainty. We consider macroe

In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability measures. Furthermore, we also consider worst-case of weight

In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index $H \in (0, 1)$ under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about stochastic calculus with respect to a fractional G-Brownian

Complex adaptive learning is intelligent. It is adaptive, learns in feedback loops, and generates hidden patterns as many individuals, elements or particles interact in complex adaptive systems (CAS). CAS highlights adaptation in life and lifeless complex systems cutting across all traditional natur

Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events, systemic risk methodologies utilise advanced mathematical and compu

We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition on the underlying weight function. As an application, we sho

We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients admit closed-form solutions. The mean control is identical to d

The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices. Fudenberg et al. (2015) develop the additive perturbed utility

This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio selection is interconnected through relative performance conc

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging stra

We study the mean field limit of a rank-based model with common noise, which arises as an extension to models for the market capitalization of firms in stochastic portfolio theory. We show that, under certain conditions on the drift and diffusion coefficients, the empirical cumulative distribution f

The integration of thematic satellite allocations into core-satellite portfolio architectures is commonly approached using factor exposures, discretionary convictions, or backtested performance, with feasibility assessed primarily through liquidity screens or market-impact considerations. While such

We study the excess growth rate – a fundamental logarithmic functional arising in portfolio theory – from the perspective of information theory. We show that the excess growth rate can be connected to the Rényi and cross entropies, the Helmholtz free energy, L. Campbell’s measure of average code len

The Santa Fe model is an established econophysics model for describing stochastic dynamics of the limit order book from the viewpoint of the zero-intelligence approach. While its foundation was studied by combining a dimensional analysis and a mean-field theory by E. Smith et al. in Quantitative Fin

In continuous time, the laws of martingales tend to be singular to each other. Notably, N. Gantert introduced the concept of specific relative entropy between real-valued continuous martingales, defined as a scaling limit of finite-dimensional relative entropies, and showed that this quantity is non

Financial markets have long since been modeled using stochastic methods such as Brownian motion, and more recently, rough volatility models have been built using fractional Brownian motion. This fractional aspect brings memory into the system. In this project, we describe and analyze a financial mod

This paper presents a theoretical extension of the DeTEcT framework proposed by Sadykhov et al., DeTEcT, where a formal analysis framework was introduced for modelling wealth distribution in token economies. DeTEcT is a framework for analysing economic activity, simulating macroeconomic scenarios, a

Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the USA-China trade

Models for spin systems known from statistical physics are used in econometrics in the form of agent-based models. Econophysics research in econometrics is increasingly developing general market models that describe exchange phenomena and use the chemical potential $μ$ known from physics in the cont

We study the roles of social and individual learning on outcomes of the Minority Game model of a financial market. Social learning occurs via agents adopting the strategies of their neighbours within a social network, while individual learning results in agents changing their strategies without inpu

We study an information acquisition problem in which an informed trader acquires costly information prior to trading in the Kyle equilibrium. The cost of information acquisition is represented by an entropy cost. Regardless of the prior distribution of the asset payoff, continuous signals are optima

We study the Merton portfolio management problem within a complete market, non constant time discount rate and general utility framework. The non constant discount rate introduces time inconsistency which can be solved by introducing sub game perfect strategies. Under some asymptotic assumptions on

Two novel and direct quantum mechanical representations of the Black-Scholes model are constructed based on the (Wick-rotated) quantization of two specific mechanical systems. The quantum setup is achieved by means of the associated Laplace-Beltrami operator (one for each model), and not by merely a

We consider a stochastic volatility model where the price evolution depend on the exponential of the Ornstein–Uhlenbeck process. After a brief revision of the related theory the entropy-minimal equivalent martingale measure. is calculated.

The real estate sector is one of the key drivers of India’s national economy, contributing about 7.3% to the GDP. As the market evolves, more players enter, and government policies become more stringent, Indian real estate companies face increasing competition. Improving financial competitiveness i

In several recent works on infinite-dimensional systems of ODEs \cite{cao_derivation_2021,cao_explicit_2021,cao_iterative_2024,cao_sticky_2024}, which arise from the mean-field limit of agent-based models in economics and social sciences and model the evolution of probability distributions (on the s

Income inequality and redistribution policies are modeled with a minimal, endogenous model of a simple foraging economy. Significant income inequalities emerge from the model for populations of equally capable individuals presented with equal opportunities. Stochastic income distributions from the m

This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval Δ results in the random properties of price and return. We describe how average

In Chakraborti’s yard-sale model of an economy, identical agents engage in trades that result in wealth exchanges, but conserve the combined wealth of all agents and each agent’s expected wealth. In this model, wealth condensation, that is, convergence to a state in which one agent owns everything a

We synthesize and discuss some new developments in econophysics. In doing so, we focus on option pricing. We relax the assumptions of constant volatility and interest rate. In doing so, we rely on the square root of the Brownian motion. We also provide simple, closed-form pricing formulas for the Am

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, b

Models for spin systems known from statistical physics are applied by analogy in econometrics in the form of agent-based models. Researchers suggest that the state variable temperature $T$ corresponds to volatility $σ$ in capital market theory problems. To the best of our knowledge, this has not yet

Caratheodory’s axiom of adiabatic inaccessibility states that, in any neighborhood of a thermodynamic state, certain states remain unreachable via adiabatic processes. Non-arbitrage mirrors this topological restriction in finance. Preserving this constraint in resource-limited systems identifies the

We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more flexible alternative to classical methods in terms of modellin

Financial markets convert the incremental arrival of information into asset price changes. In a sandpile model grains of sand represent bits of data, and the size of an avalanche, governed by a scaling law, is linked to price volatility. While this model of self-organized criticality reproduces styl

Random walk models with log-normal outcomes fit local market observations remarkably well. Yet interconnected or recursive structures - layered derivatives, leveraged positions, iterative funding rounds - periodically produce power-law distributed events. We show that the transition from log-normal

This study explores the application of Hawkes processes to model high-frequency data in the context of limit order books. Two distinct Hawkes-based models are proposed and analyzed: one utilizing exponential kernels and the other employing power-law kernels. These models are implemented within a biv

We introduce a novel framework for developing fully-automated trading model algorithms. Unlike the traditional approach, which is grounded in analytical complexity favored by most quantitative analysts, we propose a paradigm shift that embraces real-world complexity. This approach leverages key conc

A money transfer involves a buyer and a seller. A buyer buys goods or services from a seller. The money the buyer decreases is the same as that the seller increases. At each time step, a pair of socially connected agents are selected and transact in agreed money. We evolve the Deffuant model to a mo

There are multiple explanations for stylized facts in high-frequency trading, including adaptive and informed agents, many of which have been studied through agent-based models. This paper investigates an alternative explanation by examining whether, and under what circumstances, interactions betwee

``Self-Organised Criticality’’ (SOC) is the mechanism by which complex systems spontaneously settle close to a critical point, at the edge between stability and chaos, and characterized by fat-tailed fluctuations and long-memory correlations. Such a scenario may explain why insignificant perturbat

In quantum mechanics and finance, numeraire invariance - the unobservability of absolute phase or price scale - fits with a projective and curved state space. This projective geometry has a measurable signature. For spin-one and higher spin systems, the Taylor expansion of directed distance contains

We reformulate the neutral wealth tax framework of Froeseth (2026; arXiv:2603.05264) in the language of stochastic dynamics and statistical physics. Individual wealth under geometric Brownian motion satisfies a Langevin equation with multiplicative noise; the probability density of wealth across a p

Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can take various unexpected market behaviors into account to modify

In Chakraborti’s yard-sale model of an economy, identical agents engage in pairwise trades, resulting in wealth exchanges that conserve each agent’s expected wealth. Doob’s martingale convergence theorem immediately implies almost sure wealth condensation, i.e., convergence to a state in which a sin

There seems to exist significant similarities between a reactor system and a supply chain from collection to delivery. In the reactor case, neutrons are continuously produced and absorbed in nuclear fuel. In a supply system case, items are continuously collected and continuously delivered to destina

To predict the future movements of stock markets, numerous studies concentrate on daily data and employ various machine learning (ML) models as benchmarks that often vary and lack standardization across different research works. This paper tries to solve the problem from a fresh standpoint by aiming

The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was fir

Benoit Mandelbrot’s scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a “fox” in Isaiah Berlin’s famous dichotomy of thinkers. This essay argues, however, that Mandelbrot was, at h

The proposed framework introduces a novel multidimensional representation of money using tensor analysis, enabling a more granular examination of economic interactions and capital flow. By treating money as a multidimensional entity, this approach allows for detailed tracking and modeling of sectora

Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a microsystem. From a macroscopically point of view, it is import