1
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Zhong G, Li JC. Multiple stochastic and inverse stochastic resonances with transition phenomena in complex corporate financial systems. CHAOS (WOODBURY, N.Y.) 2024; 34:063115. [PMID: 38838105 DOI: 10.1063/5.0198165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 05/15/2024] [Indexed: 06/07/2024]
Abstract
This study examines the role of periodic information, the mechanism of influence, stochastic resonance, and its controllable analysis in complex corporate financial systems. A stochastic predator-prey complex corporate financial system model driven by periodic information is proposed. Additionally, we introduce signal power amplification to quantify the stochastic resonance phenomenon and develop a method for analyzing stochastic resonance in financial predator-prey dynamics within complex corporate financial systems. We optimize a simplified integral calculation method to enhance the proposed model's performance, which demonstrates superiority over benchmark models based on empirical evidence. Based on stochastic simulations and numerical calculations, we can observe multiple stochastic and multiple inverse stochastic resonances. Furthermore, variations in initial financial information, periodic information frequency, and corporate growth capacity induced stochastic resonance and inverse stochastic resonance. These variations also led to state transitions between the two resonance behaviors, indicating transition phenomena. These findings suggest the potential for regulating and controlling stochastic and inverse stochastic resonance in complex corporate finance, enabling controllable stochastic resonance behaviors.
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Affiliation(s)
- Guangyan Zhong
- School of Finance, Yunnan University of Finance and Economics, Kunming 650221, People's Republic of China
| | - Jiang-Cheng Li
- School of Finance, Yunnan University of Finance and Economics, Kunming 650221, People's Republic of China
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2
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Chen F, Kou Z, Jiang Z, Guo W, Liu X. Physical Limit of Nonlinear Brownian Oscillators in Quantum Trap. J Phys Chem Lett 2024; 15:1719-1725. [PMID: 38320267 DOI: 10.1021/acs.jpclett.3c03334] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
Quantum trap, a quantum and thermal fluctuations-induced nonmonotonous potential, offers a chance to build up microscopic mechanical systems completely dominated by fluctuations. Here, we explore the physical limit of the effective damping ratio of the nonlinear Brownian oscillator in a quantum trap, set by the finite separation for avoiding molecular-scale effects on the trap potential and the surface confinement effect-induced diverging damping and random forces. The quasiharmonic approximations and Langevin dynamics simulations show that the lowest effective damping ratios of the suspended Au plate and Au sphere upon a Teflon coating of 10 nm can be ∼210 and ∼145, respectively, at room temperature. Perforation is proposed as an effective route to reduce the damping ratio (down to 6.4) by attenuating the surface confinement effect. An unexpected result due to the temperature dependences of dielectric function and viscosity of ethanol is a further reduced damping ratio at 400 K (1.3). The nonlinear Brownian oscillator in the quantum trap shows promise of probing near-boundary hydrodynamics at nanoscale.
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Affiliation(s)
- Fangyuan Chen
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016
| | - Zepu Kou
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016
| | - Zonghuiyi Jiang
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016
| | - Wanlin Guo
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016
| | - Xiaofei Liu
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016
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3
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Abril FS, Quimbay CJ. Evolution of temporal fluctuation scaling exponent in nonstationary time series using supersymmetric theory of stochastic dynamics. Phys Rev E 2024; 109:024112. [PMID: 38491575 DOI: 10.1103/physreve.109.024112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Accepted: 01/18/2024] [Indexed: 03/18/2024]
Abstract
Temporal fluctuation scaling (TFS) is an emergent property of complex systems that relates the variance (Ξ_{2}) and the mean (M_{1}) from an empirical data set in the form Ξ_{2}∼M_{1}^{α_{TFS}}, where the dispersion (fluctuation) of the data has been described in terms of Ξ_{2}. At present, it has been shown that this law of complex systems has different multidisciplinary applications such as characterizing the market rate based on its exponent, explaining the spatial spread of a pandemic or measuring dispersion in a counting process, among others, if it is known how the average value M_{1} of a representative quantity in a system changes. Then, using the path integral formalism and Parisi-Sourlas method, we propose an extension of path integral formalism to understand the origin of the temporal fluctuation scaling and the evolution of its exponent over time in nonstationary time series. To this end, we first show how the probability of transition between two states of a stochastic variable x(t) can be expressed once it is known its cumulant generating function. Also, we introduce a nonlinear term in a cumulant generating function of the form H^{(n)}(p,t;γ)∼p^{n} to obtain a model where the nth moment of the probability distribution evolves arbitrarily. Subsequently, in order to reproduce the temporal fluctuation scaling, a linear combination of H^{(n)}(p,t;γ) with n∈{1,2} is used. Therefore this allows describing how the mean M_{1}(t) and the variance Ξ_{2}(t) of empirical time series evolve. Thence, an analytical expression is deduced for the evolution of the temporal evolution of the temporal fluctuation scaling exponent α_{TFS}(t). Likewise, the validity of the expression found for α_{TFS}(t) is verified with a toy model based on white noise. Finally, this approach is verified in two stock indices (Dow Jones and Sao Paulo stock index) and two currencies (GBP-USD and EUR-USD) with daily data. It is found that this approach accurately captures the evolution of the mean and variance of these four financial derivatives after contrasting the results with a coefficient of determination that depends on H^{(n)}(p,t;γ). Also, it is shown that the temporal fluctuation scaling exponent is a measure of uncertainty or volatility in financial time series.
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Affiliation(s)
- F S Abril
- Universidad Nacional de Colombia, Departamento de Física, Bogotá D.C. 111321, Colombia
| | - C J Quimbay
- Universidad Nacional de Colombia, Departamento de Física, Bogotá D.C. 111321, Colombia
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4
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Stoll EA. A thermodynamical model of non-deterministic computation in cortical neural networks. Phys Biol 2023; 21:016003. [PMID: 38078366 DOI: 10.1088/1478-3975/ad0f2d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Accepted: 11/23/2023] [Indexed: 12/18/2023]
Abstract
Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of non-deterministic computation. A mean field approach is used, with the trial Hamiltonian maximizing available free energy and minimizing the net quantity of entropy, compared with a reference Hamiltonian. Thermodynamic quantities are always conserved during the computation; free energy must be expended to produce information, and free energy is released during information compression, as correlations are identified between the encoding system and its surrounding environment. Due to the relationship between the Gibbs free energy equation and the Nernst equation, any increase in free energy is paired with a local decrease in membrane potential. As a result, this process of thermodynamic computation adjusts the likelihood of each neuron firing an action potential. This model shows that non-deterministic signaling outcomes can be achieved by noisy cortical neurons, through an energy-efficient computational process that involves optimally redistributing a Hamiltonian over some time evolution. Calculations demonstrate that the energy efficiency of the human brain is consistent with this model of non-deterministic computation, with net entropy production far too low to retain the assumptions of a classical system.
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Affiliation(s)
- Elizabeth A Stoll
- Western Institute for Advanced Study, Denver, Colorado, United States of America
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5
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Yang GH, Ma SQ, Bian XD, Li JC. The roles of liquidity and delay in financial markets based on an optimal forecasting model. PLoS One 2023; 18:e0290869. [PMID: 37656682 PMCID: PMC10473490 DOI: 10.1371/journal.pone.0290869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2022] [Accepted: 08/17/2023] [Indexed: 09/03/2023] Open
Abstract
We investigate the roles of liquidity and delay in financial markets through our proposed optimal forecasting model. The efficiency and liquidity of the financial market are examined using stochastic models that incorporate information delay. Based on machine learning, we estimate the in-sample and out-of-sample forecasting price performances of the six proposed methods using the likelihood function and Bayesian methods, and the out-of-sample prediction performance is compared with the benchmark model ARIMA-GARCH. We discover that the forecasting price performance of the proposed simplified delay stochastic model is superior to that of the benchmark methods by the test methods of a variety of loss function, superior predictive ability test (SPA), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Using data from the Chinese stock market, the best forecasting model assesses the efficiency and liquidity of the financial market while accounting for information delay and trade probability. The rise in trade probability and delay time affects the stability of the return distribution and raises the risk, according to stochastic simulation. The empirical findings show that empirical and best forecasting approaches are compatible, that company size and liquidity (delay time) have an inverse relationship, and that delay time and liquidity have a nonlinear relationship. The most efficient have optimal liquidity.
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Affiliation(s)
- Guo-Hui Yang
- School of Finance, Yunnan University of Finance and Economics, Kunming, P. R. of China
| | - Si-Qi Ma
- School of Finance, Yunnan University of Finance and Economics, Kunming, P. R. of China
| | - Xiao-Dong Bian
- School of Finance, Yunnan University of Finance and Economics, Kunming, P. R. of China
| | - Jiang-Cheng Li
- School of Finance, Yunnan University of Finance and Economics, Kunming, P. R. of China
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Grimaudo R, Valenti D, Spagnolo B, Troisi A, Filatrella G, Guarcello C. Axion Field Influence on Josephson Junction Quasipotential. MATERIALS (BASEL, SWITZERLAND) 2023; 16:5972. [PMID: 37687664 PMCID: PMC10488603 DOI: 10.3390/ma16175972] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 08/23/2023] [Accepted: 08/29/2023] [Indexed: 09/10/2023]
Abstract
The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.
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Affiliation(s)
- Roberto Grimaudo
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
| | - Davide Valenti
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
| | - Bernardo Spagnolo
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
- Radiophysics Department, Lobachevskii State University of Nizhnii Novgorod, 23 Gagarin Ave., Nizhnii Novgorod 603950, Russia
| | - Antonio Troisi
- Department of Sciences and Technologies, University of Sannio, Via De Sanctis, 82100 Benevento, Italy;
| | - Giovanni Filatrella
- Department of Sciences and Technologies, University of Sannio, Via De Sanctis, 82100 Benevento, Italy;
- Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, 80126 Napoli, Italy
| | - Claudio Guarcello
- Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, 80126 Napoli, Italy
- Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy
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7
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Ndjomatchoua FT, Gninzanlong CL, Djomo TLMM, Kepnang Pebeu MF, Tchawoua C. Diversity-enhanced stability. Phys Rev E 2023; 108:024206. [PMID: 37723729 DOI: 10.1103/physreve.108.024206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
We give compelling evidence that diversity, represented by a quenched disorder, can produce a resonant collective transition between two unsteady states in a network of coupled oscillators. The stability of a metastable state is optimized and the mean first-passage time maximized at an intermediate value of diversity. This finding shows that a system can benefit from inherent heterogeneity by allowing it to maximize the transition time from one state to another at the appropriate degree of heterogeneity.
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Affiliation(s)
- Frank Thomas Ndjomatchoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Carlos Lawrence Gninzanlong
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Thierry Landry Michel Mbong Djomo
- Department of Civil Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. Box 39, Bambili, Bamenda, Cameroon
| | - Maxime Fabrice Kepnang Pebeu
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
| | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Ngoa Ekelle, Yaoundé, Cameroon
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Hosseini R, Tajik S, Koohi Lai Z, Jamali T, Haven E, Jafari R. Quantum Bohmian-Inspired Potential to Model Non-Gaussian Time Series and Its Application in Financial Markets. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1061. [PMID: 37510008 PMCID: PMC10378105 DOI: 10.3390/e25071061] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 06/21/2023] [Accepted: 06/24/2023] [Indexed: 07/30/2023]
Abstract
We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.
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Affiliation(s)
- Reza Hosseini
- Department of Physics, Shahid Beheshti University, Evin, Tehran 1983969411, Iran
| | - Samin Tajik
- Physics Department, Brock University, St. Catharines, ON L2S 3A1, Canada
| | - Zahra Koohi Lai
- Department of Physics, Islamic Azad University, Firoozkooh Branch, Firoozkooh 3981838381, Iran
| | - Tayeb Jamali
- Porous Media Research Lab, Department of Geology, Kansas State University, Manhattan, KS 66506, USA
| | - Emmanuel Haven
- Faculty of Business Administration, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada
| | - Reza Jafari
- Department of Physics, Shahid Beheshti University, Evin, Tehran 1983969411, Iran
- Institute of Information Technology and Data Science, Irkutsk National Research Technical University, Lermontova St., 664074 Irkutsk, Russia
- Center for Communications Technology, London Metropolitan University, London N7 8DB, UK
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9
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Stojkoski V, Jolakoski P, Pal A, Sandev T, Kocarev L, Metzler R. Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210157. [PMID: 35400188 DOI: 10.1098/rsta.2021.0157] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual to change their position in the income rankings. For this purpose, we use the properties of an established model for income growth that includes 'resetting' as a stabilizing force to ensure stationary dynamics. We find that the dynamics of inequality is regime-dependent: it may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodicity. Mobility measures, conversely, are always stable over time, but suggest that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the income share of the top earners in the USA, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterizes inequality and immobility. Our results can serve as a simple rationale for the observed real-world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.
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Affiliation(s)
- Viktor Stojkoski
- Faculty of Economics, Ss. Cyril and Methodius University, Skopje 1000, Macedonia
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, Skopje 1000, Macedonia
- Center for Collective Learning, ANITI, University of Toulouse, 31000 Toulouse, France
| | - Petar Jolakoski
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, Skopje 1000, Macedonia
- Association for Research and Analysis-ZMAI, Skopje 1000, Macedonia
| | - Arnab Pal
- Department of Physics, Indian Institute of Technology, Kanpur, Kanpur 208016, India
- Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Trifce Sandev
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, Skopje 1000, Macedonia
- Institute of Physics & Astronomy, University of Potsdam, Potsdam-Golm 14776, Germany
- Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, Skopje 1000, Macedonia
| | - Ljupco Kocarev
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, Skopje 1000, Macedonia
- Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, PO Box 393, Skopje 1000, Macedonia
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, Potsdam-Golm 14776, Germany
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Xu WJ, Zhong LX. Market impact shapes competitive advantage of investment strategies in financial markets. PLoS One 2022; 17:e0260373. [PMID: 35113865 PMCID: PMC8812846 DOI: 10.1371/journal.pone.0260373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 11/08/2021] [Indexed: 11/18/2022] Open
Abstract
The formation of an efficient market depends on the competition between different investment strategies, which accelerates all available information into asset prices. By incorporating market impact and two kinds of investment strategies into an agent-based model, we have investigated the coevolutionary mechanism of different investment strategies and the role of market impact in shaping a competitive advantage in financial markets. The coevolution of history-dependent strategies and reference point strategies depends on the levels of market impact and risk tolerance. For low market impact and low risk tolerance, the majority-win effect makes the trend-following strategies become dominant strategies. For high market impact and low risk tolerance, the minority-win effect makes the trend-rejecting strategies coupled with trend-following strategies become dominant strategies. The coupled effects of price fluctuations and strategy distributions have been investigated in depth. A U-shape distribution of history-dependent strategies is beneficial for a stable price, which is destroyed by the existence of reference point strategies with low risk tolerance. A δ-like distribution of history-dependent strategies leads to a large price fluctuation, which is suppressed by the existence of reference point strategies with high risk tolerance. The strategies that earn more in an inefficient market lose more in an efficient market. Such a result gives us another explanation for the principle of risk-profit equilibrium in financial markets: high return in an inefficient market should be coupled with high risk in an efficient market, low return in an inefficient market should be coupled with low risk in an efficient market.
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Affiliation(s)
- Wen-Juan Xu
- School of Law, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China
| | - Li-Xin Zhong
- School of Finance and Coordinated Innovation Center of Wealth Management and Quantitative Investment, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China
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11
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Zhang C, Yang T, Qu SX. Impact of time delays and environmental noise on the extinction of a population dynamics model. THE EUROPEAN PHYSICAL JOURNAL. B 2021; 94:219. [PMID: 34751210 PMCID: PMC8565651 DOI: 10.1140/epjb/s10051-021-00219-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 09/27/2021] [Indexed: 06/13/2023]
Abstract
ABSTRACT In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.
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Affiliation(s)
- Chun Zhang
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062 People’s Republic of China
| | - Tao Yang
- Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072 People’s Republic of China
| | - Shi-Xian Qu
- School of Physics and Information Technology, Shaanxi Normal University, Xi’an, 710062 People’s Republic of China
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12
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Abril FS, Quimbay CJ. Temporal fluctuation scaling in nonstationary time series using the path integral formalism. Phys Rev E 2021; 103:042126. [PMID: 34005870 DOI: 10.1103/physreve.103.042126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 03/30/2021] [Indexed: 11/07/2022]
Abstract
We model the time evolution of the mean and the variance of nonstationary time series using the path integral formalism with the purpose to obtain the temporal fluctuation scaling presents in complex systems. To this end, we first show how the probability of change between two times of a stochastic variable can be written in terms of a Feynman kernel, where the cumulant generating function of statistical moments is identified as the Hamiltonian of the system. Thus, by including the effects of a stochastic drift and a temporal logarithmic term in the cumulant generating function, we find analytical expressions describing the temporal evolutions of the mean and the variance in terms of cumulants. Starting from these expressions, we obtain the temporal fluctuation scaling written as a general analytical relation between the variance and the mean, in such a way that this relation satisfies a power law, with the exponent being a function on time. Additionally, we study several financial time series associated with changes of prices for some stock indexes and currencies. For this financial time series, we find that the temporal evolution of the mean and the variance, the temporal fluctuation scaling, and the temporal evolution of the exponent which are obtained from this path integral approach are in agreement with those obtained using the empirical data.
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Affiliation(s)
- F S Abril
- Universidad Nacional de Colombia, Departamento de Física, Bogotá, D.C., Colombia
| | - C J Quimbay
- Universidad Nacional de Colombia, Departamento de Física, Bogotá, D.C., Colombia
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13
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James N, Menzies M. Association between COVID-19 cases and international equity indices. PHYSICA D. NONLINEAR PHENOMENA 2021; 417:132809. [PMID: 33362322 PMCID: PMC7756167 DOI: 10.1016/j.physd.2020.132809] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 11/17/2020] [Accepted: 11/17/2020] [Indexed: 05/03/2023]
Abstract
This paper analyzes the impact of COVID-19 on the populations and equity markets of 92 countries. We compare country-by-country equity market dynamics to cumulative COVID-19 case and death counts and new case trajectories. First, we examine the multivariate time series of cumulative cases and deaths, particularly regarding their changing structure over time. We reveal similarities between the case and death time series, and key dates that the structure of the time series changed. Next, we classify new case time series, demonstrate five characteristic classes of trajectories, and quantify discrepancy between them with respect to the behavior of waves of the disease. Finally, we show there is no relationship between countries' equity market performance and their success in managing COVID-19. Each country's equity index has been unresponsive to the domestic or global state of the pandemic. Instead, these indices have been highly uniform, with most movement in March.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Sydney, NSW, Australia
| | - Max Menzies
- Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
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14
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Molina-Muñoz J, Mora-Valencia A, Perote J. Market-crash forecasting based on the dynamics of the alpha-stable distribution. PHYSICA A 2020; 557:124876. [PMID: 32834434 PMCID: PMC7320685 DOI: 10.1016/j.physa.2020.124876] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Revised: 05/22/2020] [Indexed: 06/11/2023]
Abstract
This paper investigates on the alpha-stable distribution capacity to capture the probability of market crashes by means of the dynamic forecasting of its alpha and beta parameters. On the basis of the GARCH-stable model, we design a market crash forecasting methodology that involves three-stepwise procedure: (i) Recursively estimation the GARCH-stable parameters through a rolling window; (ii) alpha-stable parameters forecasting according to a VAR model; and (iii) Crash probabilities forecasting and analysis. The model performance for alternative crash definitions is assessed in terms of different accuracy criteria, and compared with a random walk model as benchmark. Our applications to a wide variety of stock indexes for developed and emerging markets reveals a high degree of accuracy and replicability of the results. Hence the model represents an interesting tool for risk management and the design of early warning systems for future crashes.
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Affiliation(s)
- Jesús Molina-Muñoz
- Universidad de los Andes, School of Management, Calle 21 No. 1-20, Bogotá, Colombia
| | - Andrés Mora-Valencia
- Universidad de los Andes, School of Management, Calle 21 No. 1-20, Bogotá, Colombia
| | - Javier Perote
- University of Salamanca (IME), Campus Miguel de Unamuno (Edif. F.E.S.), 37007 Salamanca, Spain
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15
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Sun Y, Bozdogan H. Segmentation of High Dimensional Time-Series Data Using Mixture of Sparse Principal Component Regression Model with Information Complexity. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1170. [PMID: 33286939 PMCID: PMC7597341 DOI: 10.3390/e22101170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 09/16/2020] [Accepted: 10/13/2020] [Indexed: 06/12/2023]
Abstract
This paper presents a new and novel hybrid modeling method for the segmentation of high dimensional time-series data using the mixture of the sparse principal components regression (MIX-SPCR) model with information complexity (ICOMP) criterion as the fitness function. Our approach encompasses dimension reduction in high dimensional time-series data and, at the same time, determines the number of component clusters (i.e., number of segments across time-series data) and selects the best subset of predictors. A large-scale Monte Carlo simulation is performed to show the capability of the MIX-SPCR model to identify the correct structure of the time-series data successfully. MIX-SPCR model is also applied to a high dimensional Standard & Poor's 500 (S&P 500) index data to uncover the time-series's hidden structure and identify the structure change points. The approach presented in this paper determines both the relationships among the predictor variables and how various predictor variables contribute to the explanatory power of the response variable through the sparsity settings cluster wise.
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Affiliation(s)
| | - Hamparsum Bozdogan
- Department of Business Analytics and Statistics, University of Tennessee, Knoxville, TN 37996, USA;
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16
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A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets. MATHEMATICS 2020. [DOI: 10.3390/math8081216] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs.
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17
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Petrović I, Jeknić-Dugić J, Arsenijević M, Dugić M. Dynamical stability of the weakly nonharmonic propeller-shaped planar Brownian rotator. Phys Rev E 2020; 101:012105. [PMID: 32069583 DOI: 10.1103/physreve.101.012105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Indexed: 11/07/2022]
Abstract
Dynamical stability is a prerequisite for control and functioning of desired nanomachines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped planar rotator. To match certain expected realistic physical situations, we consider a weakly nonharmonic external potential for the rotator. Two methods for investigating stability are used. First, we employ a quantum-mechanical counterpart of the so-called "first passage time" method. Second, we investigate time dependence of the standard deviation of the rotator for both the angle and angular momentum quantum observables. A perturbationlike procedure is introduced and implemented to provide the closed set of differential equations for the moments. Extensive analysis is performed for different combinations of the values of system parameters. The two methods are, in a sense, mutually complementary. Appropriate for the short time behavior, the first passage time exhibits a numerically relevant dependence only on the damping factor as well as on the rotator size. However, the standard deviations for both the angle and angular momentum observables exhibit strong dependence on the parameter values for both short and long time intervals. Contrary to our expectations, the time decrease of the standard deviations is found for certain parameter regimes. In addition, for certain parameter regimes nonmonotonic dependence on the rotator size is observed for the standard deviations and for the damping of the oscillation amplitude. Hence, nonfulfillment of the classical expectation that the size of the rotator can be reduced to the inertia of the rotator. In effect, the task of designing the desired protocols for the proper control of the molecular rotations becomes an optimization problem that requires further technical elaboration.
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Affiliation(s)
- Igor Petrović
- University of Niš, Faculty of Science and Mathematics, Višegradska 33, 18000 Niš, Serbia
| | - Jasmina Jeknić-Dugić
- University of Niš, Faculty of Science and Mathematics, Višegradska 33, 18000 Niš, Serbia
| | - Momir Arsenijević
- University of Kragujevac, Faculty of Science, Radoja Domanovića 12, 34000 Kragujevac, Serbia
| | - Miroljub Dugić
- University of Kragujevac, Faculty of Science, Radoja Domanovića 12, 34000 Kragujevac, Serbia
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18
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Filatrella G, De Liso N. Predicting one type of technological motion? A nonlinear map to study the ‘sailing-ship’ effect. Soft comput 2019. [DOI: 10.1007/s00500-019-04622-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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19
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Peng Y, Albuquerque PHM, do Nascimento IF, Machado JVF. Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis. ENTROPY 2019; 21:e21040376. [PMID: 33267090 PMCID: PMC7514861 DOI: 10.3390/e21040376] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Revised: 03/29/2019] [Accepted: 04/04/2019] [Indexed: 11/16/2022]
Abstract
This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz’s portfolio allocation model, evaluating the technique’s performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance.
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Affiliation(s)
- Yaohao Peng
- Campus Universitário Darcy Ribeiro-Brasília, University of Brasilia, Brasilia 70910-900, Brazil
- Correspondence:
| | | | - Igor Ferreira do Nascimento
- Campus Universitário Darcy Ribeiro-Brasília, University of Brasilia, Brasilia 70910-900, Brazil
- Federal Institute of Piauí, Rua Álvaro Mendes, 94-Centro (Sul), Teresina-PI 64001-270, Brazil
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