Psychophysics of time perception and valuation in temporal discounting of gain and loss

Anomalies in intertemporal choice (e.g. “hyperbolic” discounting and sign effect) have been investigated in econophysics and behavioral neuroeconomics. We experimentally examined the roles of psychophysical effects of time perception and subjective valuation of outcomes (value function) on temporal discounting of gain and loss, by utilizing a q$q$-exponential temporal discounting model developed in Tsallis’s thermostatistics. Consequently, we demonstrated that both “hyperbolic” discounting and the sign effect (i.e. gain is more steeply time-discounted than loss) are due to psychophysical effects of time perception (i.e., nonlinearity and gain–loss asymmetry). Implications of the present study for neuroeconomics and econophysics are discussed.     

A probabilistic choice model based on Tsallis’ statistics

Decision under risk and uncertainty (probabilistic choice) has been attracting attention in econophysics and neuroeconomics. This paper proposes a probabilistic choice model based on a mathematical equivalence of delay and uncertainty in decision-making, and the deformed algebra developed in the Tsallis’ non-extensive thermodynamics. Furthermore, it is shown that this model can be utilized to quantify the degree of consistency in probabilistic choice in humans and animals. Future directions in the application of the model to studies in econophysics, neurofinance, neuroeconomics, and social physics are discussed.     

Tsallis’ non-extensive free energy as a subjective value of an uncertain reward

Recent studies in neuroeconomics and econophysics revealed the importance of reward expectation in decision under uncertainty. Behavioral neuroeconomic studies have proposed that the unpredictability and the probability of an uncertain reward are distinctly encoded as entropy and a distorted probability weight, respectively, in the separate neural systems. However, previous behavioral economic and decision-theoretic models could not quantify reward-seeking and uncertainty aversion in a theoretically consistent manner. In this paper, we have: (i) proposed that generalized Helmholtz free energy in Tsallis’ non-extensive thermostatistics can be utilized to quantify a perceived value of an uncertain reward, and (ii) empirically examined the explanatory powers of the models. Future study directions in neuroeconomics and econophysics by utilizing the Tsallis’ free energy model are discussed.     

A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics

Impulsivity and inconsistency in intertemporal choice (discounting) have drawn attention in econophysics and neuroeconomics. Although it is well established that most people often show irrational discounting (e.g., hyperbolic discounting), little is known regarding whether the irrationality is mitigated or not, when the choice was performed by someone else instead of subject herself. This point is important for economic policy-making. In order to compare consistency and impulsivity in choices for oneself versus someone else, we experimentally estimated the consistency parameter q in Tsallis’ statistics-based discount function for oneself and someone else, by assessing the points of subjective equality (indifference points) at 7 delays (1 week to 25 years) in humans. We observed that (i) most people are more inconsistent when the outcomes of intertemporal choice are only relevant to someone else (q=−8.89) than when relevant to oneself (q=−2.63), and (ii) impulsivity, distinguished from inconsistency by utilizing the Tsallis statistics-based q-exponential discount function, is also larger in the choice for someone else than for oneself. Our results indicate that (i) leaving decision-making processes with some others may neither reduce impulsivity nor correct inconsistency and (ii) when q-exponential discounting is utilized, the definition range of q-parameter should be extended to q<0, and smaller (q<1) and larger (q>1) values indicate more inconsistent discounting. Together, the usefulness of the q-exponential discounting for analyzing the dynamic consistency of economic policy was demonstrated in the present study.     

Progress in physical properties of Chinese stock markets

In the past two decades, statistical physics was brought into the field of finance, applying new methods and concepts to financial time series and developing a new interdiscipline “econophysics”. In this review, we introduce several commonly used methods for stock time series in econophysics including distribution functions, correlation functions, detrended fluctuation analysis method, detrended moving average method, and multifractal analysis. Then based on these methods, we review some statistical properties of Chinese stock markets including scaling behavior, long-term correlations, cross-correlations, leverage effects, antileverage effects, and multifractality. Last, based on an agent-based model, we develop a new option pricing model — financial market model that shows a good agreement with the prices using real Shanghai Index data. This review is helpful for people to understand and research statistical physics of financial markets.     

Is econophysics a new discipline? The neopositivist argument

Econophysics is a new approach which applies various models and concepts associated with statistical physics to economic (and financial) phenomena. This field of research is a new step in the history and the evolution of Physics Sciences and the question about the disciplinary characteristics of this field must be asked. At first glance, it might appear that economics and econophysics share the same subject of research (that of analysis of economic reality). In this paper I will use neopositivism to show that econophysics is methodologically very different from economics and that it can be considered as a separate discipline. The neopositivist framework provides econophysics with some arguments for rejecting mainstream economics.     

金融物理的若干基本问题与研究进展(Ⅰ)--价格的统计分析与价格涨落的随机过程模型

金融物理学是物理学概念和方法应用于金融分析的一门新的交叉学科，近年来受到人们的广泛关注．文章简述了金融物理的研究方向和研究方法，重点讨论了价格涨落的统计分析和相关的物理模型．     

Market dynamics and stock price volatility

This paper presents a possible explanation for some of the empirical properties of asset returns within a heterogeneous-agents framework. The model turns out, even if we assume the input fundamental value follows an simple Gaussian distribution lacking both fat tails and volatility dependence, these features can show up in the time series of asset returns. In this model, the profit comparison and switching between heterogeneous play key roles, which build a connection between endogenous market and the emergence of stylized facts.Received: 21 January 2004, Published online: 12 July 2004PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 87.23.Ge Dynamics of social systems - 05.10.-a Computational methods in statistical physics and nonlinear dynamics     

Multistability of impact, utility and threshold concepts of binary choice models

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.     

Effects of saving and spending patterns on holding time distribution

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed.Received: 4 September 2003, Published online: 19 November 2003PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 87.23.Ge Dynamics of social systems - 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 02.50.-r Probability theory, stochastic processes, and statistics     

金融风险管理与物理学家

作为经济物理学的一个重要专题,文章简要介绍了金融风险管理的基本框架和主要内容,包括风险界定、风险来源、风险度量、风险处置等.特别地,展示了物理学在金融风险管理中的可能应用,讨论了物理学家对金融风险管理可能做出的贡献.     

Stokes integral of economic growth: Calculus and the Solow model

Economic growth depends on capital and labor and two-dimensional calculus has been applied to economic theory. This leads to Riemann and Stokes integrals and to the first and second laws of production and growth. The mathematical structure is the same as in thermodynamics, economic properties may be related to physical terms: capital to energy, production to physical work, GDP per capita to temperature, production function to entropy. This is called econophysics. Production, trade and banking may be compared to motors, heat pumps or refrigerators. The Carnot process of the first law creates two levels in each system: cold and hot in physics; buyer and seller, investor and saver, rich and poor in economics. The efficiency rises with the income difference of rich and poor. The results of econophysics are compared to neoclassical theory.     

Physics of risk and uncertainty in quantum decision making

The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning paradox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of the Quantum Decision Theory. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within the suggested theory. We also introduce a general methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that decay to a strictly positive constant for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal.     

Economic uncertainty and econophysics

The objective of this paper is to provide a methodological link between econophysics and economics. I will study a key notion of both fields: uncertainty and the ways of thinking about it developed by the two disciplines. After having presented the main economic theories of uncertainty (provided by Knight, Keynes and Hayek), I show how this notion is paradoxically excluded from the economic field. In economics, uncertainty is totally reduced by an a priori Gaussian framework—in contrast to econophysics, which does not use a priori models because it works directly on data. Uncertainty is then not shaped by a specific model, and is partially and temporally reduced as models improve. This way of thinking about uncertainty has echoes in the economic literature. By presenting econophysics as a Knightian method, and a complementary approach to a Hayekian framework, this paper shows that econophysics can be methodologically justified from an economic point of view.     

Statistical properties of corporate board and director networks

The boards of directors of the largest corporations of a country together with the directors form a dense bipartite network. The board network consists of boards connected through common directors. The director network is obtained taking the directors as nodes, and a membership in the same board as a link. These networks are involved in the decision making processes relevant to the macro-economy of a country. We present an extensive and comparative analysis of the statistical properties of the board network and the director network for the first 1000 US corporations ranked by revenue (Fortune 1000) in the year 1999 and for the corporations of the Italian Stock Market. We find several common statistical properties across the data sets, despite the fact that they refer to different years and countries. This suggests an underlying universal formation mechanism which is not captured in a satisfactory way by the existent network models. In particular we find that all the considered networks are Small Worlds, assortative, highly clustered and dominated by a giant component. Several other properties are examined. The presence of a lobby in a board, a feature relevant to decision making dynamics, turns out to be a macroscopic phenomenon in all the data sets.Received: 21 February 2004, Published online: 14 May 2004PACS: 87.23.Ge Dynamics of social systems - 89.65.-s Social and economic systems - 89.65.Gh Economics, econophysics, financial markets, business and management     

Coupled disease–behavior dynamics on complex networks: A review

It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease–behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease–behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.     

Evolution of networks

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.     

Rigorous Proof of the Boltzmann–Gibbs Distribution of Money on Connected Graphs

Models in econophysics, i.e., the emerging field of statistical physics that applies the main concepts of traditional physics to economics, typically consist of large systems of economic agents who are characterized by the amount of money they have. In the simplest model, at each time step, one agent gives one dollar to another agent, with both agents being chosen independently and uniformly at random from the system. Numerical simulations of this model suggest that, at least when the number of agents and the average amount of money per agent are large, the distribution of money converges to an exponential distribution reminiscent of the Boltzmann–Gibbs distribution of energy in physics. The main objective of this paper is to give a rigorous proof of this result and show that the convergence to the exponential distribution holds more generally when the economic agents are located on the vertices of a connected graph and interact locally with their neighbors rather than globally with all the other agents. We also study a closely related model where, at each time step, agents buy with a probability proportional to the amount of money they have, and prove that in this case the limiting distribution of money is Poissonian.