arXiv subjects

Sorin Solomon

Publications and source records attributed to Sorin Solomon.

At least 37 records · Page 2Linked to original sources

arXiv2005

Social Anti-Percolation and Negative Word of Mouth

Many new products fail, despite preliminary market surveys having determined considerable potential market share. This effect is too systematic to be attributed to bad luck. We suggest an explanation by presenting a new percolation theory model for product propagation, where agents interact over a social network. In our model, agents who do not adopt the product spread negative word of mouth to their neighbors, and so their neighborhood becomes less susceptible to the product. The result is a dramatic increase in the percolation threshold. When the effect of negative word of mouth is strong enough, it is shown to block any product from spreading to a significant fraction of the network. So, rather then being rejected by a large fraction of the agents, the product gets blocked by the rejection of a negligible fraction of the potential market. The rest of the potential buyers do not adopt the product because they are never exposed to it: the negative word of mouth spread by initial rejectors suffocates the diffusion by negatively affecting the immediate neighborhood of the propagation front.

cond-mat.other↗

arXiv2005

Statistical Economics on Multi-Variable Layered Networks

We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their peers' expectations (optimism/pessimism are contagious), while people living in the same neighborhood may influence their peers' saving patterns (stinginess/largeness are contagious). Thus, for each type of variable there exists a different underlying social network, which we refer to as a ``layer''. Each layer connects the same set of agents by a different set of links defining a different topology. In different layers, the nature of the variables and their dynamics may be different (Ising, Heisenberg, matrix models, etc). The different variables belonging to the same agent interact (the level of optimism of an agent may influence its saving level), thus coupling the various layers. We present a simple instance of such a network, where a one-dimensional Ising chain (representing the interaction between the optimist-pessimist expectations) is coupled through a random site-to-site mapping to a one-dimensional generalized Blume-Capel chain (representing the dynamics of the agents' saving ratios). In the absence of coupling between the layers, the one-dimensional systems describing respectively the expectations and the saving ratios do not feature any ordered phase (herding). Yet, such a herding phase emerges in the coupled system, highlighting the non-trivial nature of the present framework.

cond-mat.stat-mech↗

arXiv2005

Traders imprint themselves by adaptively updating their own avatar

Simulations of artificial stock markets were considered as early as 1964 and multi-agent ones were introduced as early as 1989. Starting the early 90's, collaborations of economists and physicists produced increasingly realistic simulation platforms. Currently, the market stylized facts are easily reproduced and one has now to address the realistic details of the Market Microstructure and of the Traders Behaviour. This calls for new methods and tools capable of bridging smoothly between simulations and experiments in economics. We propose here the following Avatar-Based Method (ABM). The subjects implement and maintain their Avatars (programs encoding their personal decision making procedures) on NatLab, a market simulation platform. Once these procedures are fed in a computer edible format, they can be operationally used as such without the need for belabouring, interpreting or conceptualising them. Thus ABM short-circuits the usual behavioural economics experiments that search for the psychological mechanisms underlying the subjects behaviour. Finally, ABM maintains a level of objectivity close to the classical behaviourism while extending its scope to subjects' decision making mechanisms. We report on experiments where Avatars designed and maintained by humans from different backgrounds (including real traders) compete in a continuous double-auction market. We hope this unbiased way of capturing the adaptive evolution of real subjects behaviour may lead to a new kind of behavioural economics experiments with a high degree of reliability, analysability and reproducibility.

cs.MA↗

arXiv2003

Socioeconomic Interaction and Swings in Business Confidence Indicators

We propose a stochastic model of interactive formation of individual expectations regarding the business climate in an industry. Our model is motivated by a business climate survey cond ucted since 1960 in Germany by the Ifo-institute (www.ifo.de). In accordance with the data structure of this survey, in our model there is asso ciated to each economic agent (business manager) a random variable with a three-element state space representing her possible types of expectations. The evolution of individual expectations in a finite population is then modeled as a spatio-temporal stochastic process with local interaction between agents. An appropriate structure of the interaction between agents in our setting turns out to be provided by a Festinger-function (in physics called energy function or Ham iltonian) of the Blume-Capel type. Time series of the fractions of agents holding each type of expectations are obtained for the model by Monte Carlo simulations. We find that our model reproduces some generic features of the empirical time series obtained from the German business-climate data, in particu lar the occurrence of abrupt large but rare swings. In our model, such swings occur as spontaneous phase changes between macroscopic states.

cond-mat.stat-mech↗

arXiv2002

Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent variables $w_i$, $i=1,...N$. The equations include a stochastic autocatalytic term (representing investments), a drift term (representing social security payments) and a time dependent saturation term (due to the finite size of the economy). The $w_i$'s turn out to exhibit a power-law distribution of the form $P(w) \sim w^{-1-α}$. It is shown analytically that the exponent $α$ can be expressed as a function of one parameter, which is the ratio between the constant drift component (social security) and the fluctuating component (investments). This result provides a link between the lower and upper cutoffs of this distribution, namely between the resources available to the poorest and those available to the richest in a given society. The value of $α$ %as well as the position of the lower cutoff is found to be insensitive to variations in the saturation term, that represent the expansion or contraction of the economy. The results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power-law distribution with $1 < α< 2$.

cond-mat.stat-mech↗

arXiv2002

Long-Time Fluctuations in a Dynamical Model of Stock Market Indices

Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable distribution L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot be expressed in a closed form, one can identify its parameters by testing the dependence of the central peak height on tau as well as the power-law decay of the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it was found that the behavior of the central peak of P(r) for the Standard & Poor 500 index is consistent with the Levy distribution with alpha=1.4. In a more recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3, thus deviating from the Levy distribution. In this paper we study the distribution of returns in a generic model that describes the dynamics of stock market indices. For the distributions P(r) generated by this model, we observe that the scaling of the central peak is consistent with a Levy distribution while the tails exhibit a power-law distribution with an exponent alpha > 2, namely beyond the range of Levy-stable distributions. Our results are in agreement with both empirical studies and reconcile the apparent disagreement between their results.

cond-mat.stat-mech↗

arXiv2001

Stochastic Multiplicative Processes for Financial Markets

We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correlation between relative updated wealths is the origin of the nontrivial properties of returns, including the power law distribution with exponent outside the stable Levy regime and the long-range persistence of volatility correlations.

cond-mat.stat-mech↗

arXiv2001

Volatility driven market in a generalised Lotka Voltera formalism

The Generalized Lotka Voltera (GLV) formalism has been introduced in order to explain the power law distributions in the individual wealth (w_i (t)) (Pareto law) and financial markets returns (fluctuations) (r) as a result of the auto-catalytic (multiplicative random) character of the individual capital dynamics. As long as the multiplicative random factor (lambda) is extracted from the same probability distribution for all the individuals, the exponent of the power laws turns out to be independent on the time variations of the average ( ). This explains also the stability over the past century of experimentally measured Pareto exponent. In contrast to the scaling properties of the single time ("unconditional") probability distributions, the (auto-)correlations between observables measured at different times are not correctly reproduced by the original GLV, if the variance (sigma^2) of $λ$ is time independent. In the GLV formalism the volatility (r^2) auto-correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent. We show in the present paper that by making the variance of the individual wealth changes (sigma^2) a function of the market volatility , one correctly reproduces the market volatility long range correlations. Moreover, we show that this non-trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non-trivial patterns in the overall market trends. If the feedback is too strong, it may even endanger the market stability.

cond-mat↗

arXiv2001

Power Laws of Wealth, Market Order Volumes and Market Returns

Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic assumptions on capital dynamics, we are able to obtain very specific predictions for the distribution of social wealth. First, we show that in a 'fair' market, the wealth distribution among individual investors fulfills a power law. We then argue that 'fair play' for capital and minimal socio-biological needs of the humans traps the economy within a power law wealth distribution with a particular Pareto exponent $α\sim 3/2$. In particular we relate it to the average number of individuals L depending on the average wealth: $α\sim L/(L-1)$. Then we connect it to certain power exponents characterising the stock markets. We obtain that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent $β\sim α\sim 3/2$. Consequently, in a market where trades take place by matching pairs of such sell and buy orders, the corresponding exponent for the market returns is expected to be of order $γ\sim 2 α\sim 3$. These results are consistent with recent experimental measurements of these power law exponents ([Maslov 2001] for $β$ and [Gopikrishnan et al. 1999] for $γ$).

cond-mat.stat-mech↗

arXiv2001

Finite market size as a source of extreme wealth inequality and market instability

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent $α$ of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that N is always finite in real systems. We show that any finite value of N leads to properties which can differ crucially from the naive theoretical results obtained by assuming an infinite N. In particular, finite N may cause in the absence of an appropriate social policy extreme wealth inequality $α< 1$ and market instability.

cond-mat.stat-mech↗

arXiv2001

Stability of Pareto-Zipf Law in Non-Stationary Economies

Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent alpha are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent alpha = 1.4 is related to built-in human social and biological constraints.

cond-mat.stat-mech↗

arXiv2000

Power Laws are Boltzmann Laws in Disguise

Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two characteristic regimes. For large values of wealth it takes the form of a Pareto style power law. For small values of wealth, (w less then wmin) the distribution function tends sharply to zero with infinite slope. The origin of this law lies in the random multiplicative process built into the model. Whilst such results have been known since the time of Gibrat, the present framework allows for a stable power law in an arbitrary and irregular global dynamics, so long as the market is `fair', i.e., there is no net advantage to any particular group or individual. We show for our model that the relative distribution of wealth follows a time independent distribution of this form even thought the total wealth may follow a more complicated dynamics and vary with time in an arbitrary manner. In developing the theory, we draw parallels with conventional thermodynamics and derive for the system the associated laws of `econodynamics' together with the associated econodynamic potentials. The power law that arises in the distribution function may then be identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. The distribution function of stock market returns for our model, it is argued, will follow the same qualitative laws and exhibit power law behaviour.

cond-mat.stat-mech↗

arXiv2000

HIV time hierarchy: Winning the war while, loosing all the battles

AIDS is the pandemic of our era. A disease that scares us not only because it is fatal but also because its insidious time course makes us all potential carriers long before it hands us our heads in a basket. The strange three stage dynamics of aids is also one of the major puzzles in describing the disease theoretically (1). Aids starts, like most diseases, in a peak of virus expression (2,3), which is practically wiped out by the immune system. However it then remains in the body at a low level of expression until later (some time years later) when there is an outbreak of the disease which terminally cripples the immune system causing death from various common pathogens. In this paper we show, using a microscopic simulation, that the time course of AIDS is determined by the interactions of the virus and the immune cells in the shape space of antigens and that it is the virus's ability to move more rapidly in this space (it's high mutability) that causes the time course and eventual 'victory' of the disease. These results open the way for further experimental and therapeutic conclusions in the ongoing battle with the HIV epidemic.

nlin.AO↗

arXiv2000

The Emergence of Spatial Complexity in the immune System

Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics of natural systems have been described using differential equations. But, differential equation models fail to account for the emergence of large-scale inhomogeneities and for the influence of inhomogeneity on the overall dynamics of biological systems. Here, we show that a microscopic simulation methodology enables us to model the emergence of large-scale objects and to extend the scope of mathematical modeling in biology. We take a simple example from immunology and illustrate that the methods of classical differential equations and microscopic simulation generate contradictory results. Microscopic simulations generate a more faithful approximation of the reality of the immune system.

cond-mat.stat-mech↗

arXiv2000

Discrete Financial Means: When exception rules, mean means nothing; Auto-catalytic Individuals Survive by all Means

The origin of macroscopic complexity is traced in a wide range of systems (imunology, ecology, finance, marketing, etc) to the discrete and auto-catalytic (i.e. multiplicative) character of their elementary components. Even in the simplest conditions which naively would lead to the complete "death" of any dynamics, these 2 properties lead to the emergence of self-organized adaptive collective objects. In turn, these objects insure the survival of a very rich and unexpectedly resilient macroscopic "life".

cond-mat.stat-mech↗

arXiv2000

Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents $α$ of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Levy regime $α< 2$, the power law decay with large exponent ($α> 2$), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.

cond-mat.stat-mech↗

arXiv2000

Microscopic Discrete Proliferating Components Cause the Self-Organized Emergence of Macroscopic Adaptive Features in Biological Systems

We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by representing individually the elementary interactions between its microscopic components (antibodies, antigens, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging over individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures. In turn the effective dynamics of these structures affects the average behavior of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behavior. Our conclusions are supported both by explicit microscopic simulations and by analytic calculations. As the optimal method we propose a mixture of microscopic simulation (MS) systems describing each reaction separately, and average methods describing the average behavior of the agents.

nlin.AO↗

arXiv2000

Market Ecology, Pareto Wealth Distribution and Leptokurtic Returns in Microscopic Simulation of the LLS Stock Market Model

The LLS stock market model is a model of heterogeneous quasi-rational investors operating in a complex environment about which they have incomplete information. We review the main features of this model and several of its extensions. We study the effects of investor heterogeneity and show that predation, competition, or symbiosis may occur between different investor populations. The dynamics of the LLS model lead to the empirically observed Pareto wealth distribution. Many properties observed in actual markets appear as natural consequences of the LLS dynamics: truncated Levy distribution of short-term returns, excess volatility, a return autocorrelation "U-shape" pattern, and a positive correlation between volume and absolute returns.

cond-mat.stat-mech↗