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We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence…

Mathematical Finance · Quantitative Finance 2017-11-22 Marian Gidea , Yuri Katz

Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…

Mathematical Finance · Quantitative Finance 2023-07-11 Miguel A. Ruiz-Ortiz , José Carlos Gómez-Larrañaga , Jesús Rodríguez-Viorato

We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological…

Mathematical Finance · Quantitative Finance 2017-01-24 Marian Gidea

In the present work we extend the Bak-Sneppen model for biological evolution by introducing local interactions between species. This ``environmental'' perturbation can modify the intrinsic fitness of each element of the ecology, leading to…

Other Condensed Matter · Physics 2010-10-14 M. Bartolozzi , D. B. Leinweber , A. W. Thomas

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…

Machine Learning · Statistics 2025-11-18 Ioannis Diamantis

Classical technical analysis methods of stock evolution are recalled, i.e. the notion of moving averages and momentum indicators. The moving averages lead to define death and gold crosses, resistance and support lines. Momentum indicators…

Condensed Matter · Physics 2009-11-07 M. Ausloos , K. Ivanova

The Prevalence of Community support and engagement for different domains in the tech industry has changed and evolved throughout the years. In this study, we aim to understand, analyze and predict the trends of technology in a scientific…

Machine Learning · Computer Science 2021-08-19 Raja CSP Raman , Rohith Mahadevan , Divya Perumal , Vedha Sankar , Talha Abdur Rahman

We investigate by numerical simulations and analytical calculations the Bak-Sneppen model for biological evolution in scale-free networks. By using large scale numerical simulations, we study the avalanche size distribution and the activity…

Statistical Mechanics · Physics 2009-11-07 Yamir Moreno , Alexei Vazquez

We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS)…

Statistical Finance · Quantitative Finance 2023-04-17 Samuel W. Akingbade , Marian Gidea , Matteo Manzi , Vahid Nateghi

Studying the micro-trading behaviors before stock price jumps is an important problem for financial regulations and investment decisions. In this study, we provide a new framework to study pre-jump trading behaviors based on multivariate…

Statistical Finance · Quantitative Finance 2021-03-01 Ao Kong , Robert Azencott , Hongliang Zhu , Xindan Li

Predicting stock price movements is a pivotal element of investment strategy, providing insights into potential trends and market volatility. This study specifically examines the predictive capacity of historical stock prices and technical…

Computational Engineering, Finance, and Science · Computer Science 2024-04-17 Morteza Maleki

The proliferation of diverse, high-leverage trading instruments in modern financial markets presents a complex, "noisy" environment, leading to a critical question: which trading strategies are evolutionarily viable? To investigate this, we…

Physics and Society · Physics 2026-04-01 Yijia Chen

Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return…

Statistical Finance · Quantitative Finance 2009-11-13 Attilio L. Stella , Fulvio Baldovin

The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of…

Adaptation and Self-Organizing Systems · Physics 2009-11-11 D. Horvath , Z. Kuscsik , M. Gmitra

Accurately predicting stock repurchases is crucial for quantitative investment and risk management, yet traditional static models fail to capture the complex temporal dependencies of corporate financial conditions. This paper proposes a…

Statistical Finance · Quantitative Finance 2026-04-14 Xiang Ao , Jingxuan Zhang , Xinyu Zhao

We investigate the performance of dynamic portfolios constructed using more than 21,000 technical trading rules on 12 categorical and country-specific markets over the 2004-2015 study period, on rolling forward structures of different…

Statistical Finance · Quantitative Finance 2019-06-14 Georgios Sermpinis , Arman Hassanniakalager , Charalampos Stasinakis , Ioannis Psaradellis

As the increasing application of AI in finance, this paper will leverage AI algorithms to examine tail risk and develop a model to alter tail risk to promote the stability of US financial markets, and enhance the resilience of the US…

Risk Management · Quantitative Finance 2025-08-08 Zong Ke , Yuchen Yin

We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Chaohong Lee , Xiwen Zhu , Kelin Gao

We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…

Statistical Finance · Quantitative Finance 2016-12-05 Mario Bonino , Matteo Camelia , Paolo Pigato

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable…

Statistical Finance · Quantitative Finance 2009-11-13 Fulvio Baldovin , Attilio L. Stella
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