اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Immediate Exchange model: an analytical investigation
121
0
0.0
(
0
)
تأليف
Guy Katriel
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the Immediate Exchange model, recently introduced by Heinsalu and Patriarca [Eur. Phys. J. B 87: 170 (2014)], who showed by simulations that the wealth distribution in this model converges to a Gamma distribution with shape parameter $2$. Here we justify this conclusion analytically, in the infinite-population limit. An infinite-population version of the model is derived, describing the evolution of the wealth distribution in terms of iterations of a nonlinear operator on the space of probability densities. It is proved that the Gamma distributions with shape parameter $2$ are fixed points of this operator, and that, starting with an arbitrary wealth distribution, the process converges to one of these fixed points. We also discuss the mixed model introduced in the same paper, in which exchanges are either bidirectional or unidirectional with fixed probability. We prove that, although, as found by Heinsalu and Patriarca, the equilibrium distribution can be closely fit by Gamma distributions, the equilibrium distribution for this model is {it{not}} a Gamma distribution.
قيم البحث
اقرأ أيضاً
Indirect competition emerged from the complex organization of human societies, and knowledge of the existing network topology may aid in developing effective strategies for success. Here, we propose an agent-based model of competition with systems co
-existing in a `small-world social network. We show that within the range of parameter values obtained from the model and empirical data, the network evolution is highly dependent on $k$, the local parameter describing the density of neighbors in the network. The model applied to language death and competition of telecommunication companies show strong correspondence with empirical data.
Swarm intelligence is widely recognized as a powerful paradigm of self-organized optimization, with numerous examples of successful applications in distributed artificial intelligence. However, the role of physical interactions in the organization of
traffic flows in ants under crowded conditions has only been studied very recently. The related results suggest new ways of congestion control and simple algorithms for optimal resource usage based on local interactions and, therefore, decentralized control concepts. Here, we present a mathematical analysis of such a concept for an experiment with two alternative ways with limited capacities between a food source and the nest of an ant colony. Moreover, we carry out microscopic computer simulations for generalized setups, in which ants have more alternatives or the alternative ways are of different lengths. In this way and by variation of interaction parameters, we can get a better idea, how powerful congestion control based on local repulsive interactions may be. Finally, we will discuss potential applications of this design principle to routing in traffic or data networks and machine usage in supply systems.
In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors
. The first one is a linear term that models the expansion of the agents economy and that is controlled by the {it growth capacity parameter}. The second one is an inhibition exponential term that is regulated by the {it local environmental pressure}. Depending on the parameter setting, the system can display Pareto or Boltzmann-Gibbs behavior in the asymptotic dynamical regime. The regions of parameter space where the system exhibits one of these two statistical behaviors are delimited. Other properties of the system, such as the mean wealth, the standard deviation and the Gini coefficient, are also calculated.
Using an artificial neural network (ANN), a fixed universe of approximately 1500 equities from the Value Line index are rank-ordered by their predicted price changes over the next quarter. Inputs to the network consist only of the ten prior quarterly
percentage changes in price and in earnings for each equity (by quarter, not accumulated), converted to a relative rank scaled around zero. Thirty simulated portfolios are constructed respectively of the 10, 20,..., and 100 top ranking equities (long portfolios), the 10, 20,..., 100 bottom ranking equities (short portfolios) and their hedged sets (long-short portfolios). In a 29-quarter simulation from the end of the third quarter of 1994 through the fourth quarter of 2001 that duplicates real-world trading of the same method employed during 2002, all portfolios are held fixed for one quarter. Results are compared to the S&P 500, the Value Line universe itself, trading the universe of equities using the proprietary ``Value Line Ranking System (to which this method is in some ways similar), and to a Martingale method of ranking the same equities. The cumulative returns generated by the network predictor significantly exceed those generated by the S&P 500, the overall universe, the Martingale and Value Line prediction methods and are not eroded by trading costs. The ANN shows significantly positive Jensens alpha, i.e., anomalous risk-adjusted expected return. A time series of its global performance shows a clear antipersistence. However, its performance is significantly better than a simple one-step Martingale predictor, than the Value Line system itself and than a simple buy and hold strategy, even when transaction costs are accounted for.
We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of log--normal and pow
er--law behaviours. We then focus on the Bouchaud--Mezard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self--organises towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log--normal or the power--law form. This means that the first--order topological properties alone (such as the scale--free property) are not enough to explain the emergence of the empirically observed emph{mixed} form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with variable density of links. We show new results detailing how this effect is related to the higher--order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
