The co-evolutionary dynamics of directed network of spin market agents

The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of dynamic directed stochastic network. The co-evolutionary principles are applied in the frame of Bak - Sneppen self-organized dynamics [P. Bak, K. Sneppen, Phys. Rev. Letter 71 (1993) 4083] that includes the processes of selection and extinction actuated by the local (node) fitness. The local fitness is related to orientation of spin agent with respect to instant magnetization. The stationary regime characterized by a fat tailed distribution of the log-price returns with index $\alpha\simeq 3.6$ (out of the Levy range) is identified numerically. The non-trivial consequence of the extremal dynamics is the partially power-law decay (an effective exponent varies between -0.3 and -0.6) of the autocorrelation function of volatility. Broad-scale network topology with node degree distribution characterized by the exponent $\gamma=1.8$ from the range of social networks is obtained.Comment: 10 pages, 4 figures. accepted for publication in Physica

Stochastic Opinion Formation in Scale-Free Networks

The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two state $\pm 1$, as a stochastic response of each of them to the opinion of his/her neighbours in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barab\'asi-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behaviour, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres

Deep learning as closure for irreversible processes: A data-driven generalized Langevin equation

The ultimate goal of physics is finding a unique equation capable of describing the evolution of any observable quantity in a self-consistent way. Within the field of statistical physics, such an equation is known as the generalized Langevin equation (GLE). Nevertheless, the formal and exact GLE is not particularly useful, since it depends on the complete history of the observable at hand, and on hidden degrees of freedom typically inaccessible from a theoretical point of view. In this work, we propose the use of deep neural networks as a new avenue for learning the intricacies of the unknowns mentioned above. By using machine learning to eliminate the unknowns from GLEs, our methodology outperforms previous approaches (in terms of efficiency and robustness) where general fitting functions were postulated. Finally, our work is tested against several prototypical examples, from a colloidal systems and particle chains immersed in a thermal bath, to climatology and financial models. In all cases, our methodology exhibits an excellent agreement with the actual dynamics of the observables under consideration

Can Google Trends search queries contribute to risk diversification?

Portfolio diversification and active risk management are essential parts of financial analysis which became even more crucial (and questioned) during and after the years of the Global Financial Crisis. We propose a novel approach to portfolio diversification using the information of searched items on Google Trends. The diversification is based on an idea that popularity of a stock measured by search queries is correlated with the stock riskiness. We penalize the popular stocks by assigning them lower portfolio weights and we bring forward the less popular, or peripheral, stocks to decrease the total riskiness of the portfolio. Our results indicate that such strategy dominates both the benchmark index and the uniformly weighted portfolio both in-sample and out-of-sample.Comment: 11 pages, 3 figure

Agent-Based Computational Economics: A Brief Guide to the Literature

Agent-based computational economics (ACE)is the computational study of economies modelled as evolving systems of autonomous interacting agents. This short paper is a brief guide to recent ACE research. For more information, visit the ACE Web site at http://www.econ.iastate.edu/tesfatsi/ace.htm. Resources available at the ACE Web site include surveys, an annotated syllabus of readings, software, teaching materials, pointers to research on economic and social network formation, and pointers to individual researchers and research groups.Agent-based computational economics