Bargaining in endogenous trading networks

We study a model in which heterogeneous agents first form a trading network where linking costs are positive but infinitesimally small. Then, a seller and a buyer are randomly selected among the agents to bargain through a chain of intermediaries. We determine both the trading path and the allocation of the surplus among the seller, the buyer and the intermediaries at equilibrium. We show that, under the initiator bargaining protocol, a trading network is pairwise stable if it is a core–periphery network where the core consists of all impatient agents who are linked to each other and the periphery consists of all patient agents who have a single link towards an impatient agent. Once agents do not know the impatience of other agents, each bilateral bargaining session may involve delay. Then, core–periphery networks may not be pairwise stable because agents may prefer to add links for reducing the length of trading paths and so avoiding costly delays in reaching a global agreement.     

具有不完全信息的内部交易动态博弈

在Kyle模型中的线性均衡假设进行了修正的基础上,针对内部交易者只具有资产价值不完全信息情况,建立两期风险厌恶型内部交易均衡模型,并求得该模型的子博弈纳什均衡解.由此发现资产价值不完信息中噪音对市场干扰程度愈小(波动程度愈小),就愈有利于内部交易者的收益;内部交易者的交易就愈活跃;交易均衡价格包含资产价值信息就愈多.     

具有比例摩擦金融市场的一般经济均衡与资产定价(英文)

本文建立具有比例摩擦金融市场的简单两时期模型．经济人具有均值－方差偏好,并且在交易金融资产的过程中支付交易费用．本文证明了两种金融资产的一般经济均衡与资产定价的基本估值公式．     

不完全实物资产市场一般货币均衡的性质(英文)

本文讨论不完全实物资产市场一般货币均衡．我们考察货币作为交换媒介的作用并且通过（规范化的）（无套利）GEI均衡与（规范化的）（无套利）一般货币均衡的等价性证明不完全实物资产市场货币交换经济一般货币均衡的性质，即普适存在性、有限性和正则性．     

带风险指数的金融均衡的存在性定理及其结构特征（上）

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、应资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Ｄｕｆｆｉｅ，Ｄ＆Ｗ．Ｓｈｆｅｒ（１９８５）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下含随机风险因素的情形，也适用于商品空间为无限维的情形．除此之外，还给出了怎样判别资产结构是否属于Ｔ类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均衡分配不确定性的度却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

考虑相对业绩的最优投资选择博弈问题研究

研究了具有相互作用的两个竞争机构投资者之间的离散时间最优投资选择博弈问题,每个机构投资者都考虑其竞争对手的相对业绩.机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择投资组合策略使得期望终端绝对财富和相对财富的效用最大.首先,定义了Nash均衡投资组合选择策略.然后,在机构投资者具有指数效用函数的假设下,得到了Nash均衡投资组合选择策略和值函数的显示表达式,分析了机构投资者之间的竞争对Nash均衡投资组合选择策略的影响.最后,通过数值计算给出了各种情况下Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系.结果表明:机构投资者之间的竞争会影响其对风险的承担,投资机会集对机构投资者的Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系会产生很大的影响.     

Supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey model

We study the local dynamics and supercritical Neimark‐Sacker bifurcation of a discrete‐time Nicholson‐Bailey host‐parasitoid model in the interior of . It is proved that if α>1, then the model has a unique positive equilibrium point , which is locally asymptotically focus, unstable focus and nonhyperbolic under certain parametric condition. Furthermore, it is proved that the model undergoes a supercritical Neimark‐Sacker bifurcation in a small neighborhood of the unique positive equilibrium point , and meanwhile, the stable closed curve appears. From the viewpoint of biology, the stable closed curve corresponds to the period or quasiperiodic oscillations between host and parasitoid populations. Some numerical simulations are presented to verify theoretical results.     

Option pricing for large agents

This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.     

A STEADY-STATE SATISFACTORY SOLUTION TO AN ENVIRONMENTAL GAME WITH PIECE-WISE DEFINED PAYOFFS

We model a pollution accumulation process through a nonlinear, nondifferentiable state equation and also as dependent on an environmental levy. Then the payoff function to an economic agent is defined piece-wise. However, for a simple demand and cost structure, the combined payoff function of all agents is diagonally strictly concave. This implies that a steady-state Nash equilibrium is unique and can be controlled by the levy. We analytically compute a steady-state Nash equilibrium solution for the agents, and use a Decision Support Tool to determine a satisfactory solution for the interactions between the agents and a legislator responsible for the levy.     

Determination of the Probability Distribution Measures from Market Option Prices Using the Method of Maximum Entropy in the Mean

Abstract

We consider the problem of recovering the risk-neutral probability distribution of the price of an asset, when the information available consists of the market price of derivatives of European type having the asset as underlying. The information available may or may not include the spot value of the asset as data. When we only know the true empirical law of the underlying, our method will provide a measure that is absolutely continuous with respect to the empirical law, thus making our procedure model independent. If we assume that the prices of the derivatives include risk premia and/or transaction prices, using this method it is possible to estimate those values, as well as the no-arbitrage prices. This is of interest not only when the market is not complete, but also if for some reason we do not have information about the model for the price of the underlying.     

Financial market equilibria with heterogeneous agents: CAPM and market segmentation

We consider a single-period financial market model with normally distributed returns and heterogeneous agents. Specifically, some investors are classical expected utility maximizers whereas some others follow cumulative prospect theory. Using well-known functional forms for the preferences, we analytically prove that a Security Market Line Theorem holds. This implies that capital asset pricing model is a necessary (though not sufficient) requirement in equilibria with positive prices. We prove that equilibria may not exist and we give explicit sufficient conditions for an equilibrium to exist. To circumvent the complexity arising from the interaction of heterogeneous agents, we propose a segmented-market equilibrium model where segmentation is endogenously determined.     

带风险指数的金融均衡的存在性定理及其结构特征(下)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

The equity risk premium and the riskfree rate in an economy with borrowing constraints

Our objective is to study analytically the effect of borrowing constraints on asset returns. We explicitly characterize the equilibrium for an exchange economy with two agents who differ in their risk aversion and are prohibited from borrowing. In a representative-agent economy with CRRA preferences, the Sharpe ratio of equity returns and the riskfree rate are linked by the risk aversion parameter. We show that allowing for preference heterogeneity and imposing borrowing constraints breaks this link. We find that an economy with borrowing constraints exhibits simultaneously a relatively high Sharpe ratio of stock returns and a relatively low riskfree interest rate, compared to both representative-agent and unconstrained heterogeneous-agent economies.      

Learning Equilibrium Play: A Myopic Approach

We model repeated play of noncooperative stage games in terms of approximate gradient steps. That simple format requires little information and no optimization. Moreover, it allows players to evaluate marginal cost or profit inexactly and to move with different velocities. Uncertainty can also be accommodated. Granted some crucial stability, we show that play converges to Nash equilibrium.     

不完全大金融市场均衡的存在性

在Aumann的大经济框架下,构造了大金融经济模型;在常规条件下,证明了具有可测空间经纪人的不完全市场均衡的存在性.由于均衡性讨论是在资产结构不完全条件下展开,与张国胜(1998,2000)的工作相比,主要结论不仅拓展了模型的经济适用范围,而且实现了方法上的突破.     

跳扩散模型下的非零和随机微分投资组合博弈

现实经济中,当股票价格受到一些重大信息影响而发生突发性的跳跃时,用跳扩散过程来描述股票价格的趋势更符合实际情况。基于这一观察,本文研究跳扩散模型下包含两个投资者的非零和投资组合博弈问题。假设金融市场中包含一种无风险资产和一种风险资产,其中风险资产的价格动态用跳扩散模型来描述。将该非零和博弈问题构造成两个效用最大化问题,每个投资者的目标是最大化终端时刻自身财富与其竞争对手财富差的均值-方差效用。运用随机控制理论,得到了均衡投资策略以及相应值函数的解析表达。最后通过数值仿真算例分析了模型相关参数变动对均衡投资策略的影响。仿真结果显示:当股价发生不连续跳跃,投资者在构造投资策略时考虑跳跃风险可以显著增加其效用水平;同时,随着博弈竞争的加剧,投资者为了在竞争中取得更好的表现,往往会采取更加激进的投资策略,增加对风险资产的投资。     

基于投资者情绪的市场均衡分析

在行为金融研究框架下,通过分析情绪投资者与理性投资者的市场均衡条件,构建基于投资者情绪的资产定价模型,并对模型进行了数值模拟。结果表明,投资者情绪是影响资产价格的重要因素:被情绪投资者高估的资产,其回报将下降;被情绪投资者低估的资产,其回报将增加;资产回报的变化程度与情绪投资者卖出低估资产的份额正相关,与资产预期回报金额的相关系数负相关;并且,乐观情绪与悲观情绪对资产价格的作用是非对称的。     

基于学习的互利协调与互制均衡及其矢量分析

纳什均衡代表了博弈参与人如何博弈的一致性预测.但是,有限理性的博弈者一般不会在一次博弈中取得一致性预期,他们总是通过不断的重复学习,使得预期逐渐向均衡方向演化.对互利协调与互制均衡进行分析,并探讨协调和均衡的动态形成机理.互制均衡强调自我实现,倾向个体利益最优.互利协调在强调自我实现的基础上,注重双赢,引导合作.现代博弈学习理论正是从有限理性的实际出发,通过学习和进化,最终实现博弈的均衡或协调.这对于如何走出传统博弈的困境具有重要意义.     

A chaotic system with only one stable equilibrium

If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one stable equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single stable node-focus equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the equilibrium is changed from an unstable saddle-focus to a stable node-focus, therefore the familiar Ši’lnikov homoclinic criterion is not applicable, it is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.     

A projected gradient dynamical system modelling the dynamics of bargaining

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations that do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world, and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents, beliefs during the bargaining period and is constructed so that an agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.