Shannon Entropy: An Econophysical Approach to Cryptocurrency Portfolios

Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide on-line availability, increasing capitalization, and potential profits. In the econophysics tradition, we show that many of the most available cryptocurrencies have return statistics that do not follow Gaussian distributions, instead following heavy-tailed distributions. Entropy measures are applied, showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.     

Convergence to an exponential wealth distribution in a random market model

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.     

相互作用herding模型的非线性行为和动力学特性

相互作用herding模型定性上能很好地呈现一些真实的经济规律,但定量上与真实的市场还有一定的距离,特别是收益绝对值的自关联衰退得太快．通过数值模拟研究发现该模型在它的参数取某些特定值时具有特有的非线性行为和动力学特性．此时,它不仅重现该模型原有的动力学特性,并能展现出更接近真实的市场规律,其中收益绝对值表现出长程关联,呈现出幂指数分布,它的幂明显变小,落在真实的市场规律范围内．     

金融市场的宏观建模和微观建模——从金融海啸与市场风险谈起

金融市场是一个复杂系统,高风险大波动危象频仍,而传统经济金融理论对此无能为力.文章从复杂性科学视角出发,通过市场宏观建模,描绘出当前金融海啸一幅泡沫演化和湮灭的图像.文章进一步论述了一个基于市场微观模型的计算实验金融学框架,认为金融学应当重建唯象学框架,并指出金融物理学在经济学科学革命中的重要性.     

金融市场中幂律分布的经验和理论研究进展--经济物理学研究的一个前沿

对金融市场波动性的研究是经济物理(econophysics)的一个重要内容．物理学家们借鉴物理学研究方法对金融市场中的主要变量进行的经验研究，揭示了金融资产价格涨落及相关变量概率分布尾部的幂律渐近行为、这一性质明显有悖于传统金融学中的正态分布和试图取代它的列维分布，引起人们广泛的兴趣．文章集中介绍了关于金融资产收益率分布尾部幂律性质经验研究的主要方法和结果，以及几种相关的理论解释．     

Size matters: some stylized facts of the stock market revisited

We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company capitalization. We show that the second moment of the traded value distribution is finite. Consequently, the Hurst exponents for the corresponding time series can be calculated. These are, however, non-universal: The persistence grows with larger capitalization and this results in a logarithmically increasing Hurst exponent. A similar trend is displayed by intertrade time intervals. Finally, we demonstrate that the distribution of the intertrade times is better described by a multiscaling ansatz than by simple gap scaling.     

Modeling the net flows of U.S. mutual funds with stochastic catastrophe theory

Using the recent work of Hartelman, van der Maas, and Wagenmakers, we demonstrate the use of invariant stochastic catastrophe models in finance for modeling net flows (the difference between purchases and redemptions of fund shares) of U.S. mutual funds. We validate Goetzmann et al. and others' work concerning the importance of sentiment variables on stock fund flows. We also answer some of the questions Goetzmann et al. and Brown et al. pose at the end of their respective papers. We end with possible experiments for experimental economists and sociophysicists.     

The effect of the topology on the spatial ultimatum game

In this work we present an analysis of a spatially non homogeneous ultimatum game. By considering different underlying topologies as substrates on top of which the game takes place we obtain nontrivial behaviors for the evolution of the strategies of the players. We analyze separately the effect of the size of the neighborhood and the spatial structure. Whereas this last effect is the most significant one, we show that even for disordered networks and provided the neighborhood of each site is small, the results can be significantly different from those obtained in the case of fully connected networks.     

Toy models and stylized realities

I discuss the role of toy models as theoretical tools for understanding complex systems of interacting agents. I review some concrete examples, in order to illustrate how this approach is able to capture, though in an admittedly stylized way, the interactions and non-linearities which are responsible for the rich phenomenology observed in reality. This allows one to interpret the system's behavior in terms of phase transitions and critical phenomena.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.