金融物理的若干基本问题与研究进展(Ⅱ)--基于经纪人的动力学模型的建模与分析

一门全新的交叉学科金融物理研究的第二种处理方法是构建金融市场物理模型，文章对其基本观点作了简介，并重点介绍了金融市场中基于经纪人的动力学模型的建模与分析，阐述了物理学在21世纪的金融工程研究中可发挥的作用与意义。     

推广的EZ模型中的普适性行为

探讨了推广EZ模型的可能性,并给出了相应的模型中人群大小分布函数的形式解.研究表明金融市场中不同大小的人群数目的交易人的数目在重新标度后将具有最广泛的普适性行为 关键词： 金融物理 人群效应 主方程     

规范场理论和金融市场模型

文章介绍近年理论物理在金融学市场建模中的应用的一个新方向，与一般的数学建模不同，它是应用几何结构的模型，建立在规范场的物理思想和纤维丛的几何结构的基础上，文章介绍了规范场的物理概念思想原则，也介绍纤维丛数学概念和几何结构，然后说明规范场理论与纤维丛理论的相结合，成为与金融市场概念和运作相匹配的市场模型，举出这一模型成功引导出金融市场产品定价的Black—Scholes方程和公式。文章对象以物理学者为主，对于理论经济学、金融理论和系统科学的读者来说可略去数学推导。     

从金融海啸看百年来物理与金融的三次交汇

  2008年由美国次级贷款引起的全球金融海啸,不仅使美国金融系统发生 “多米诺骨牌”效应,多家投资银行和商业银行相继倒闭,而且还在全球引发“蝴蝶效应”,像一个无底“黑洞”正在无情地吞食着人类的财富,谁还会在这场危机中倒下我们无从猜测。次级贷款是指还贷质量不好的贷款,是容易违约的贷款,其结构大致是这样的：美国房贷机构针对收入较低、信用记录较差的人群专门设计出的一种特别的房贷。精明的华尔街精英将这些次级贷款进行资产证券化,即将房贷变成一种可替代的、可转换的有价工具（债券）,并且进行不断分级形成形形色色的债券池,打包重组成金融衍生产品向外出售,试图通过证券化过程将风险分散、转移。正是证券化（金融创新）刺激了次级贷款泛滥,次级贷款总共达1万多亿美元,而金融衍生产品的杠杆作用导致金融风险呈几何级数放大,仅美国政府承诺的救市资金总额已达9.9万亿美元。金融衍生产品估值是基于牛顿经典力学范式,由一些非常复杂的金融物理模型（连续线性模型）做出来的,建立次级贷款金融产品的依据就是假设美国的房产价格总是上升的,客观地说,建模者是深知其模型风险的严重性的,但为了牟取暴利,顾不得那么多了。又由于监管者水平落后,面对越来越复杂的金融衍生产品已无所适从,加上在关键环节又得不到有效的监管。在监管不到位的情况下,建模者却在最大限度地增进自身效用的同时做出不利于他人的行动,过度“玩火”导致失控,给投资者造成巨大的损失和灾难。更为严重的是,建模者（国际金融炒家）已经形成为金融利益集团。总之,这次金融海啸的深层原因应该是道德风险与监管缺失和滞后,是建模者的道德观念的失败;另一方面,这次金融海啸实际上也暴露出目前金融物理理论和方法的弱点,面对现实非线性金融市场复杂系统,这样的模型是不可能跟踪预测到金融危机爆发的临界点的,难以预防和抵御到金融市场的风险的。     

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.     

经纪人模仿在演化少数者博弈模型中引入的自组织分离效应

引入真实金融市场中普遍存在的模仿机理,提出并研究了一种新的演化少数者博弈模型.在该模型中,所有的经纪人排列成满足一维周期性条件的链并有一个共同的策略.每个经纪人有一个概率p值,作决定时以概率p选择策略预测的取胜方,以概率1-p作出相反的决定,同时经纪人可以模仿财富高于自己的最近邻邻居的p值.数值模拟结果显示,通过演化使得经纪人组成的系统自组织分离成由极端行为表征的相反人群.模仿引起的演化可以明显提高系统的协作. 关键词： 科学与社会 自组织系统     

从“问题情境”到“物理图景”的关键——建立合理的物理模型

一般的物理习题都是命题者根据自己头脑中的一个理想化物理模型,结合某些问题情境和物理条件而拟定出来的.解题过程就是还原命题者物理模型的过程,也就是把实际问题模型化,把具体问题抽象成熟悉的典型物理问题.模型化是物理解题中的一种普遍方法.     

金融动力学的时空关联与大波动特性——兼谈中西方金融市场的对比研究

文章扼要地评述了金融物理学研究进展,介绍了文章作者在金融动力学时空关联方面的最新研究成果,特别关注中西方金融市场的对比研究.唯象理论研究表明,西方金融市场的价格收益率和波动率的时间关联显示杠杆效应,而中国金融市场则显示反杠杆效应;一种价格收益率和波动率的反馈相互作用可以解释杠杆和反杠杆效应的起源.西方金融市场的个体股票价格的交叉关联呈现标准的行业板块结构,而中国金融市场展示的是一种特殊的板块结构,如"ST板块"和"蓝筹板块"等.股票价格大波动可分为动力学内部产生的和外部事件诱导的两大类.金融动力学的时间反演不对称性,主要来源于外部事件诱导的大波动.     

一门新兴的交叉学科--经济物理

从上世纪90年代后期，美国科学家H．Stanley等人第一次使用“经济物理”(Econophysics国内有些论文与著作将其译为“金融物理”)这个名词以来，这个领域吸引了许多物理学家与数学家的关心，并召开了多次有关这方面的学术会议．“经济物理”顾名思义就是用物理学中的概念、方法和理论来定量地研究经济领域中，特别是金融市场内存在的复杂关系，并希望能从中寻找出某些内在的规律．面对这样一个新的研究领域，必然会有一些最基本的问题摆在人们的面前．一个问题是复杂的金融市场有什么特点，为什么可以用研究自然现象的物理工具来研究它?     

绿色数据中心流量感知虚拟机迁移(英文)

绿色数据中心内将虚拟机迁移并整合到更少数目的物理机上,从而关闭或睡眠空闲的物理机,是非常高效的数据中心节能方法.本文构建了新的流量感知虚拟机迁移模型,把物理机使用数量、流量代价、迁移代价影响都置入模型,使得虚拟机的迁移方案达到缩减物理机目的的同时,减少网络代价和迁移过程中的代价。提出了最小流量代价优先匹配的贪婪算法来解决这个多目标优化问题。仿真结果显示,这个多目标的优化中,多个优化目标之间存在一定的冲突,因此需要折中处理。该算法在物理机数量和迁移代价两个目标上做出了微小的让步,得到了较好的流量代价优化。实际的迁移算法应用中,还应考虑各个部分的真实能耗,采取合理的折中处理.     

Coupled effects of market impact and asymmetric sensitivity in financial markets

By incorporating market impact and asymmetric sensitivity into the evolutionary minority game, we study the coevolutionary dynamics of stock prices and investment strategies in financial markets. Both the stock price movement and the investors’ global behavior are found to be closely related to the phase region they fall into. Within the region where the market impact is small, investors’ asymmetric response to gains and losses leads to the occurrence of herd behavior, when all the investors are prone to behave similarly in an extreme way and large price fluctuations occur. A linear relation between the standard deviation of stock price changes and the mean value of strategies is found. With full market impact, the investors tend to self-segregate into opposing groups and the introduction of asymmetric sensitivity leads to the disappearance of dominant strategies. Compared with the situations in the stock market with little market impact, the stock price fluctuations are suppressed and an efficient market occurs. Theoretical analyses indicate that the mechanism of phase transition from clustering to self-segregation in the present model is similar to that in the majority–minority game and the occurrence and disappearance of efficient markets are related to the competition between the trend-following and the trend-aversion forces. The clustering of the strategies in the present model results from the majority-wins effect and the wealth-driven mechanism makes the market become predictable.     

Self-organized networks of competing boolean agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.     

Sub-strategy updating evolution in minority game

In this paper, we propose and study a new evolution model of minority game. Any strategy in minority game can be regarded as composed of sub-strategies corresponding to different histories. Based on the evolution model proposed by Li－Riolo－Savit, in which those agents that perform poorly may update their strategies randomly. This paper presents a new evolution model in which poor agents update their strategies by changing only a part of sub-strategy sets with low success rate. Simulation result shows that the new model with sub-strategy-set updating evolution mechanism may approach its steady state more quickly than the Li－Riolo－Savit model. In the steady state of the new model, stronger adaptive cooperation among agents will appear, implying that the social resource can be allocated more rationally and utilized more effectively compared with the Li－Riolo－Savit model.     

A competitive game whose maximal Nash-equilibrium payoff requires quantum resources for its achievement

While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting. We construct a competitive game between four players based on the minority game where the maximal Nash-equilibrium payoff when played with the appropriate quantum resource is greater than that obtainable by classical means, assuming a local hidden variable model.     

Competitive agents in a market: Statistical physics of the minority game

A brief review is presented of the minority game, a simple frustrated many-body system stimulated by considerations of a market of competitive speculative agents. Its cooperative behaviour exhibits phase transitions and both ergodic and non-ergodic regimes. It provides novel challenges to statistical physics, reminiscent of those of mean-field spin glasses.     

Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency

Using the minority game as a model for competition dynamics, we investigate the effects of interagent communications across a network on the global evolution of the game. Agent communication across this network leads to the formation of an influence network, which is dynamically coupled to the evolution of the game, and it is responsible for the information flow driving the agents' actions. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a scale-free robust leadership structure. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.     

Analysis of price behavior in lazy $-game

A non-cooperative iterated multiagent game, called a minority game, and its variations have been extensively studied in this decade. To increase its market similarity, a $-game was presented by observing the current and the next agent’s payoffs. However, since the $-game is defined as an offline game, it is difficult to simulate it in practice. So we propose a new online version of the $-game, called a lazy $-game, and analyze the price behavior of the game. First, we reveal the condition of a bubble phenomenon in the lazy $-game. Next, we investigate the price behavior in the lazy $-game and show that there are some upper/lower bounds of the price as long as both the buyers group and the sellers group are nonempty. Then, we consider the similarity between the lazy $-game and the $-game. Finally, we present some simulation results.     

Constrained information minority game: How was the night at El Farol?

We introduce a variation of the El Farol Game in which the only players who surely know the outcome of the last turn of the game are those who actually attended the bar. Other players may receive this information with reduced probability. This information can be transmitted by another player who actually attended the bar in the last turn of the game or from the media. We show that since this game is not organized around the socially optimal point, arbitrage opportunities may arise. Therefore, we study how these opportunities can be exploited by an agent. An interesting application of this model is the market of goods being auctioned, such as cars being repossessed. The results obtained here seem to closely reflect the dynamics of this market in Brazil.     

Global optimization of minority game by intelligent agents

We propose a new model of minority game with intelligent agents who use trail and error method to make a choice such that the standard deviation σ² and the total loss in this model reach the theoretical minimum values in the long time limit and the global optimization of the system is reached. This suggests that the economic systems can self-organize into a highly optimized state by agents who make decisions based on inductive thinking, limited knowledge, and capabilities. When other kinds of agents are also present, the simulation results and analytic calculations show that the intelligent agent can gain profits from producers and are much more competent than the noise traders and conventional agents in original minority games proposed by Challet and Zhang.     

Successful strategies in repeated minority games

The minority game is an important example of a non-cooperative n-person game, which can be applied on different situations with social and economic contexts. We analysed the minority game as an elementary traffic scenario in which human participants had to choose 100 times between a road A and a road B. In each period, the road, which was chosen by the minority of players won. At first view, there seems to be no outstandingly advisable strategy for the participants to enhance their payoffs because both roads have the same properties. However, an important observation is that the number of road changes of a participant is negatively correlated to his/her cumulative payoff. On average, subjects with high numbers of road changes received less money than participants who stoically chose the same road. Furthermore one could increase the coordination of the players by providing the players distribution on both roads in the last period.