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M. Rodriguez-Achach

Publications and source records attributed to M. Rodriguez-Achach.

10 recordsLinked to original sources
arXiv2014

Wealth distribution of simple exchange models coupled with extremal dynamics

Punctuated Equilibrium (PE) states that after long periods of evolutionary quiescence, species evolution can take place in short time intervals, where sudden differentiation makes new species emerge and some species extinct. In this paper, we introduce and study the effect of punctuated equilibrium on two different asset exchange models: The yard sale model (YS, winner gets a random fraction of a poorer player's wealth) and the theft and fraud model (TF, winner gets a random fraction of the loser's wealth). The resulting wealth distribution is characterized using the Gini index. In order to do this, we consider PE as a perturbation with probability $ρ$ of being applied. We compare the resulting values of the Gini index at different increasing values of $ρ$ in both models. We found that in the case of the TF model, the Gini index reduces as the perturbation $ρ$ increases, not showing dependence with the agents number. While for YS we observe a phase transition which happens around $ρ_c=0.79$. For perturbations $ρ<ρ_c$ the Gini index reaches the value of one as time increases (an extreme wealth condensation state), whereas for perturbations bigger or equal than $ρ_c$ the Gini index becomes different to one, avoiding the system reaches this extreme state. We show that both simple exchange models coupled with PE dynamics give more realistic results. In particular for YS, we observe a power low decay of wealth distribution.

physics.soc-ph↗
arXiv2010

Class formation in a social network with asset exchange

We study two kinds of economic exchange, additive and multiplicative, in a system of N agents. The work is divided in two parts, in the first one, the agents are free to interact with each other. The system evolves to a Boltzmann-Gibbs distribution with additive exchange and condenses with a multiplicative one. If bankruptcy is introduced, both types of exchange lead to condensation. Condensation times have been studied. In the second part, the agents are placed in a social network. We analyze the behavior of wealth distributions in time, and the formation of economic classes was observed for certain values of network connectivity.

q-fin.TR↗
arXiv2007

Assessing symmetry of financial returns series

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic Tn are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.

physics.data-an↗
arXiv2006

Evidence of Increment of Efficiency of the Mexican Stock Market Through the Analysis of its Variations

It is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries. In this work, we present an analysis of the variations and autocorrelations of the Mexican Stock Market index (IPC) for different periods of its historical daily data, showing evidence that the Mexican Stock Market has been increasing its efficiency in recent times. We have analyzed the returns autocorrelation function (ACF) and used detrended fluctuation analysis (DFA) methods. We also analyze the volatility of the IPC and the Dow Jones Industrial Average (DJIA) and compare their evolution. The data samples analyzed here, correspond to daily values of the IPC and DJIA for the period 10/30/1978 to 02/28/2006.

physics.soc-ph↗
arXiv2005

Condensation in an Economic Model with Brand Competition

We present a linear agent based model on brand competition. Each agent belongs to one of the two brands and interacts with its nearest neighbors. In the process the agent can decide to change to the other brand if the move is beneficial. The numerical simulations show that the systems always condenses into a state when all agents belong to a single brand. We study the condensation times for different parameters of the model and the influence of different mechanisms to avoid condensation, like anti monopoly rules and brand fidelity.

physics.soc-ph↗
arXiv2005

The distribution of wealth in the presence of altruism for simple economic models

We study the effect of altruism in two simple asset exchange models: the yard sale model (winner gets a random fraction of the poorer player's wealth) and the theft and fraud model (winner gets a random fraction of the loser's wealth). We also introduce in these models the concept of bargaining efficiency, which makes the poorer trader more aggressive in getting a favorable deal thus augmenting his winning probabilities. The altruistic behavior is controlled by varying the number of traders that behave altruistically and by the degree of altruism that they show. The resulting wealth distribution is characterized using the Gini index. We compare the resulting values of the Gini index at different levels of altruism in both models. It is found that altruistic behavior does lead to a more equitable wealth distribution but only for unreasonable high values of altruism that are difficult to expect in a real economic system.

physics.soc-ph↗
arXiv2004

Quantum and Thermal Corrections to a Classically Chaotic Dissipative System

The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the Quantum Langevin Equation formalism working on a truncated moment expansion of the density matrix of the system. We find that the type of bifurcations present in the system change upon quantization and that chaotic behavior appears for values of the nonlinear parameter that are far below the chaotic threshold for the classical model. Upon increase of temperature or Planck's constant, bifurcation points and chaotic thresholds are shifted towards lower values of the nonlinear parameter. There is also an anomalous reverse behavior for low values of the cutoff frequency.

quant-ph↗
arXiv2004

The role of mutation rate in a simple colonization model

We study the effect of mutations in a simple model of colonization, based on Montecarlo simulations. When the population colonizes the whole available habitat, a maximum population density is reached, which depends on the mutation rate. Depending on the values of other parameters, such as selection pressure, fecundity and mobility, there is an optimal value for the mutation rate for which the colonization reaches the highest density. We also investigate the survival probabilities under different conditions and its relation to the mutation rate.

q-bio.PE↗
arXiv2002

Extended States in a One-dimensional Generalized Dimer Model

The transmission coefficient for a one dimensional system is given in terms of Chebyshev polynomials using the tight-binding model. This result is applied to a system composed of two impurities located between $N$ sites of a host lattice. It is found that the system has extended states for several values of the energy. Analytical expressions are given for the impurity site energy in terms of the electron's energy. The number of resonant states grows like the number of host sites between the impurities. This property makes the system interesting since it is a simple task to design a configuration with resonant energy very close to the Fermi level $E_F$.

cond-mat.dis-nn↗