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2000, Physica A: Statistical Mechanics and its Applications
It was proved that balance equations for systems with corpuscular structure can be derived if a kinematic description by piece-wise analytic functions is available . This article presents a rigorous derivation of an one-dimensional hydrodynamic model for the stock price evolution. The kinematic description is given by a set of time functions describing the evolution of the stock price.
International Journal of Business Marketing and Management (IJBMM), 2020
Econophysics as an integrated platform of physics together with other economic sciences has a broad perspective of phenomenological physics description of the processes of economic activities. This paper suggests methods of phenomenological physics of mechanical kinematics and the model of gravitational acceleration for the description of the activity of microeconomical systems of stocks. A criterion of continuous instant stability of microeconomic systems is established by the description of the phase trajectory which is a necessary condition that this shape of the trajectory to be unchangeable with time. The conception of the econophysical acceleration is described which is related to the sold inventory. Bigger is the sold inventory then the smaller is the acceleration. The following formulation of the interconnection between the acceleration and the sold inventory is suggested: The continuous decreasing of the acceleration with time is the indicator of the continuous increasing of the sold inventory. The validation of the acceleration concept is performed by the real example of the sold inventory. The result of the average acceleration coincides with value of the rating coefficients of the stocks and respectively with the values of thermodynamical temperatures.
2005
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as general stock price formuli in closed forms which are able to generate a variety of possible price movements in time. A kind of mechanics is submitted to cover the price movements in terms of classical concepts. Where utilizing stock mechanics to grow the portfolios in real markets is also proven.
Science and culture
The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and discussed.
The scope of this paper is to present a phenomenological analysis for the time evolution of a Stock Index. The model which is introduced represents a new methodology for the description of the up and down trends of a stock index and also an example is presented referring to the Athens Stock Index (ASI). The day-by-day closing prizes of the ASI exhibit exponential laws. This behavior supports an alternative formalism based on the thermodynamic concepts of Physics in order to study the macroscopic properties of stock markets. Hence, the Newton's law of cooling is introduced as a pattern for up and down trends of the ASI. The results encourage us to construct a more complete thermodynamic model in order to understand the time evolution and the behavior of the ASI.
This paper presents an exactly solvable (by applying the fractional calculus) the rheological model of fractional dynamics of financial market conformed to the principle of no arbitrage present on financial market. The rheological model of fractional dynamics of financial market describes some singular, empirical, speculative daily peaks of stock market indices, which define crashes as a kind of phase transition. In the frame of the model the plastic market hypothesis and financial uncertainty principle were formulated, which proposed possible scenarios of some market crashes. The brief presentation of the model was made in our earlier work (and references therein). The rheological model of fractional dynamics of financial market is a deterministic model and it is complementary to already existing other ones; together with them it offers possibility for thorough and widespread technical analysis of crashes. The constitutive, fractional integral equation of the model is an analogy of the corresponding one, which defines the fractional Zener model of plastic material. The fractional Zener model is the canonical one for modern rheology, polymer physics and biophysics concerning non-Debye relaxation of viscoelastic biopolymers. The useful approximate solution of the constitutive equation of the rheological model of fractional dynamics of financial market consists of two parts: (i) the first one connected with long-term memory present in the system, which is proportional to the generalized exponential function defined by the Mittag-Leffler function and (ii) the second one describing oscillations (e.g. beats or oscillations having two slightly shifted frequences). The shape exponent leading the Mittag-Leffler function, defines here the order of the phase transition between bullish and bearish states of the financial market, in particular, for recent hossa and bessa on some small, middle and large stock markets. It happened that this solution also successfully estimated some long-term price dynamics on the hypothetical market in United States.
Stochastics and Dynamics, 2011
We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system's parameters correspond to: (a) the proportion of speculators in a market; (b) the traders' speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset's fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us ...
Physica A: Statistical Mechanics and its Applications, 2000
High-frequency data in ÿnance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well established by empirical evidence. Speciÿcally, probability distributions have the following properties: (i) They are not Gaussian and their center is well adjusted by LÃ evy distributions. (ii) They are long-tailed but have ÿnite moments of any order. (iii) They are self-similar on many time scales. Finally, (iv) at small time scales, price volatility follows a non-di usive behavior. We extend Merton's ideas on speculative price formation and present a dynamical model resulting in a characteristic function that explains in a natural way all of the above features. The knowledge of such a distribution opens a new and useful way of quantifying ÿnancial risk. The results of the model agree -with high degree of accuracy -with empirical data taken from historical records of the Standard & Poor's 500 cash index.
Arxiv preprint arXiv: …, 2011
Abstract: In this paper we present an econophysic model for the description of shares transactions in a capital market. For introducing the fundamentals of this model we used an analogy between the electrical field produced by a system of charges and the overall of ...
Physica A: Statistical Mechanics and its Applications, 1999
Several models of stock trading [P. Bak et al, Physica A 246, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H = 1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H = 1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
arXiv (Cornell University), 2009
We analyze the stability properties of equilibrium solutions and periodicity of orbits in a twodimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system's parameters correspond to: (a) the proportion of speculators in a market; (b) the traders' speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset's fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socioeconomic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are onedimensional. Our work is among the few in the area that construct and study two-dimensional dynamical systems and apply them for explanation of socioeconomic phenomena.
NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES
The solutions of many mathematical models resulting in stochastic differential equations are based on the assumption that the drift and the volatility coefficients were linear functions of the solutions. We formulated a model whose basic parameters could be derived from observations over discretized time intervals rather than the assumption that the drift and the volatility coefficients were linear functions of the solutions. We took into consideration the possibility of an asset gaining, losing or stable in a small interval of time instead of the assumption of the Binomial Asset pricing models that posited that the price could appreciate by a factor p or depreciate by a factor 1-p. A multi-dimensional stochastic differential equation was obtained whose drift is the expectation vector and the volatility the covariance of the stocks with respect to each other. The resulting system of stochastic differential equations was solved numerically using the Euler Maruyama Scheme for multi-di...
Mathematics, 2022
Exact sciences have achieved many results, validated in practice. Although their application in economics is difficult due to the human factor involved, the lack of conservation laws, and experimental difficulties, it must be highlighted that the consistent bibliography gathered in recent years in this field encourages the econophysics approach. The objective of this article is to validate and/or define a few stock strategies, based on known results from mathematics, physics, and chemistry. The scope of this research demonstrates that statistics (in portfolio theory), geometry (in technical analysis), or financial mathematics can be used in the capital market. Many of the exact science results corresponded to strategies applicable to investors. Unlike the material world, financial markets have additional components that must be considered: human psychology, sociology at the firm level, and behavioral unpredictability. The findings obtained in this research enable the enormous vastne...
Chinese Physics, 2007
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple slidingwindow algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the financial time series. By choosing suitable weighted factor for the linear approximation, the relation between the dynamical effect of restoring force and the autocorrelation of the financial time series is deduced. We especially analyze the daily log-returns of S&P 500 index from 1950 to 1999. The significance of the restoring force towards the prices evolution are investigated from its two coefficients, slope coefficient and equilibrium position. The new simple form of the restoring force obtained both from statistical and theoretical analyses suggests that the Langevin approach can effectively present the macroscopical and the detail properties of the price evolution.
Financial Assets and Investing, 2016
The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium financial market. View of the dynamic variables data was determined based on the strength of econophysical prerequisites using the model of hydrodynamic type. As a result, we found that the non-equilibrium market can be described with a good degree of accuracy with oscillator models with nonlinear rigidity and a self-oscillating system with inertial self-excitation. The most important states of model of oscillation non-equilibrium model of the market were found, including the appearance of chaos and its mechanisms. We have made the calculations of the correlation dimension for the financial time series. The results show that all observed ...
Physica A: Statistical Mechanics and its Applications, 2000
Recent observations have indicated that the traditional equilibrium market hypothesis (EMH ; also known as E cient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-ÿeld approximations like a Gaussian distribution of price uctuations. A kinetic theory for prices can be simply derived, considering in a ÿrst approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium (isothermal) equation for the price (taken as the order parameter) of a stock as a function of the volume of money available are obtained.
Mathematical Modelling, 1984
Physica A: Statistical Mechanics and its Applications, 2009
We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637 ]. The total system energy E t is shown to be proportional to a decreasing time dependent spring constant k t . This model allows to derive log-periodicity cos[log(t − t c )] on commodity prices and oscillations (surplus and shortages) in the level of stocks. We also made an attempt to connect these results to the Tsallis statistics parameter q based on a possible force-entropy correlation [Physica A 341, 165 (2004)] and find that the Tsallis second entropic term W i=1 p q i /(q − 1) relates to the square of the demand (or supply) function.
1998
Previous development of a statistical mechanics of financial markets (SMFM) is summarized in the context of generalizing a Black-Scholes model of options. Some previously published numerical issues and applications are highlighted.
Physica A-statistical Mechanics and Its Applications, 1998
A variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market. Although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic uctuations. The statistical properties of market price change can be well approximated by a simple discrete Langevin-type equation with random ampliÿcation. The macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power-law distributions in the steady state. The reason for the appearance of rapid decay in the distribution tails are discussed.
2021
Stock prices' prediction is fundamental for investment decision-making. In this research, a differential equations model is developed for stock prices prediction. More specifically, a 7×7 differential equations system based on Lanchester's combat models will be used. Data concerning the short-term stock's prices of healthcare firms listed in Athens Stock Exchange will be analyzed in order to develop and evaluate the stocks' prices predictive model. The obtained results revealed the differential equations model potential for stock prices' prediction in the short-term.
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