On the performance of West’s bubble test: A simulation approach

In this research we examine the ability of West’s bubble test [1] in detecting speculative bubbles using Brock’s (1982) [2] intertemporal general equilibrium model of asset pricing as the basis for a simulation study. In this setting, (1) the economy, by construction is efficient and produces the maximally possible amount of welfare for society, and (2) asset prices reflect the utility-maximizing behavior of consumers and the profit-maximizing behavior of firms. We find that the West’s bubble test flag as “bubbles” in the simulated data yet the data is produced from an economy in which markets are efficient in welfare production.     

An N-dimensional version of Scarf's example

This paper presents a unification of the contributions of Scarf [Some examples of global instability of competitive equilibrium, Int. Econ. Rev. 1 (1960) 157–172] and Gale [A note on global instability of competitive equilibrium, Nav. Res. Logist. Q. 10 (1963) 81–87] by means of a single class of utility functions. The unification extends Scarf's three-commodity, three-consumer economy to an n-commodity, n-consumer economy. We find that the stability of the extended economy depends on whether the law of demand for exchange economies, i.e., downward sloping excess demand, holds or not. Moreover, it is seen that there is a transition from instability to stability as substitution effect increases or as the desire of each consumer for his own commodity decreases.     

Existence of pseudo-equilibria in a financial economy

We prove the existence of a pseudo-equilibrium in a financial economy with incomplete markets in which the agents may have nonordered preferences. We use a fixed-point-like theorem of [5] that generalizes the results by Hirsch, Magill and Mas-Colell [18] and Husseini, Lasry and Magill [19] to encompass the framework considered by Gale and Mas-Colell ([14], [15]).     

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in <Emphasis Type="Italic">H</Emphasis>-spaces

In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].     

Some Results on Topological Dynamics of Antitriangular Maps

Antitriangular maps are maps of the form F(x, y) = (g(y), f(x)) defined on [0, 1] × [0, 1] which appear associated with certain models of economy and population dynamics. We study some topological dynamics properties of such maps and explore the relationship between the behavior of them and that of some connected maps defined on [0, 1].     

广义随机Solow经济增长模型

本文在文[1]的基础上进一步拓广了随机Solow经济增长模型．利用白噪声分析理论建立的广义随机Solow经济增长模型，将随机Solow模型推广到包含广义白噪声泛函及具有非可料扩散系数的情形，并且借助U—泛函方法表明了Picard迭代法在此仍十分有效．     

Bayesian abstract economies

We have a Bayesian approach for an equilibrium problem in abstract economies of the Yannelis–Prabhakar type. We consider an economy with a countable or uncountable set of agents, with private information defined by subalgebras as per Yannelis [Yannelis, A Bayesian equilibrium existence theorem, Adv. Math. Econ. 4 (2002), pp. 61–72] and the preferences defined by correspondences. We prove an existence equilibrium results which extends the known results, as Yannelis and Prabhakar theorise in [Yannelis and Prabhakar, Existence of maximal elements and equilibrium in linear topological spaces, J. Math. Econom. 12 (1983), pp. 233–245].     

Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching L��vy model

This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128–1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract.     

The arbitrage pricing theorem with incomplete preferences

This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where individuals' preferences may be incomplete or intransitive. This extends existing results to more general preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [Bewley, T. F. (2002), Knightian decision theory: part I, Decisions in Economics and Finance 25, 79–110.]. These preferences model Knightian uncertainty by preferences which may be incomplete but satisfy independence.     

A hyperspherical transformation forecasting model for compositional data

Although Aitchison’s [Aitchison, J., 1986. The Statistical Analysis of Compositional Data, Chapman and Hall, London] method of logratio transformation of compositional data is widely used in various domains, it is limited by the assumption of a strict non-negativity of the components and the requirement of special treatments in practice of the zero components. We propose a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the difficulty in maintaining non-negativity and unit-sum in forecasting compositional data over time. Applying the proposed model to a numerical simulation with a 4D compositional data embedded with zero components and forecasting the three production sectors in the Chinese economy both demonstrate the usefulness and validity of the new approach.     

Aggregate preferred correspondence and the existence of a maximin REE

A general model of a pure exchange differential information economy is studied. In this economic model, the space of states of nature is a complete probability measure space, the space of agents is a finite measure space, and the commodity space is the Euclidean space. Under some appropriate and standard assumptions on agents' characteristics, results on continuity and measurability of the aggregate preferred correspondence similar to that of Aumann [8] are established. These results together with other techniques are then employed to prove the existence of a maximin rational expectations equilibrium (maximin REE) of the economic model.     

The efficiency of remanufacturing in a dynamic input–output model

For industrialised economy of ourdays, remanufacturing represents perhaps the largest unexploited resource and opportunity for realising a greater growth of the economy in an environmental-conscious manner. The aim of this paper is to investigate of the impact of remanufacturing in the economy from an economic-efficiency point of view. In static context this phenomenon was analysed in the literature. We use the multi-sector input–output framework in a dynamic context to study intra-period relationships of the sectors of economy. We extend the classical dynamic input–output model taking into consideration the activity of remanufacturing .We try to answer the question, whether the remanufacturing/reuse increases the growth possibility of an economy. We expose a sufficient condition concerning the effectivity of an economy with remanufacturing. By this evaluation we analyse a possible sustainable development of the economy on the basis of the product recovery management of industries.     

A Markov-modulated model for stocks paying discrete dividends

We extend the model in [Korn, R., Rogers, L.C.G., 2005. Stock paying discrete dividends: modelling and option pricing. Journal of Derivatives 13, 44–49] for (discrete) dividend processes to incorporate the dependence of assets on the market mode or the state of the economy, where the latter is modeled by a hidden finite-state Markov chain. We then derive the resulting dynamics of the stock price and various option-pricing formulae. It turns out that the stock price jumps not only at the time of the dividend payment, but also when the underlying Markov chain jumps.     

Control of interconnected nonlinear delay differential equations inW 2 (1)

Our main interest in this paper is the resolution of the problem of controllability of interconnected nonlinear delay systems in function space, from which hopefully the existence of an optimal control law can be deduced later. We insist that each subsystem be controlled by its own variables while taking into account the interacting effects. This is the recent basic insight of [13] on ordinary differential systems. Controllability is deduced for the composite system from the assumption of controllability of each free subsystem and a growth condition of the interconnecting structure. Conditions for a free system’s controllability are given. One application is presented. The insight it provides for the growth of global economy has important policy implications.     

A note on Boiteux’ surplus function and dual Pareto efficiency

The purpose of this note is to study first a notion of a surplus function that originates in the work of [Boiteux, M., 1951. Le Revenu Distribuable et les Pertes Économiques. Econometrica 112–133] and to rely upon this notion to study dual Pareto efficiency in an exchange economy. This function, which we call the Boiteux’ surplus function, measures how many units of income an individual must be given to move from a reference utility level, to another utility level. We prove several properties of the Boiteux’ surplus function, and study in particular its links with the expenditure and the indirect utility functions. With regard to dual Pareto efficiency and the Boiteux’ surplus function our results are as follows. A feasible reference price–income pair is dual Pareto efficient if and only if it zero-maximizes the sum of individual Boiteux’ surplus functions among all feasible price–income pairs. We use these results to give a new proof (for the case of an exchange economy with positive prices) of the characterization by Luenberger of dual Pareto optima.     

因子分析法在中国乡镇企业发展评价中的应用

乡镇企业与区域经济发展的不和谐是造成中国区域经济发展不平衡的重要原因。本文基于《农业统计年鉴》(2006)的数据,采用因子分析法对中国30个省市的乡镇企业经济发展情况进行了统计排序,并结合区域总体经济实力予以比较。分析结果显示,各地区乡镇企业经济的发展存在不均衡性;区域内部乡镇企业经济与区域总体经济实力之间存在不协调性;中国乡镇企业经济发展与区域总体经济发展之间呈现不和谐特征。     

Specialization, inequality and the social stability of economies with collective property rights

Many, if not most, economies are observed to exhibit some form of collective ownership with some goods. These economies may fail to be socially stable, in the sense that the economy has an empty core; some groups may have an incentive to ‘recontract out’. We show that, for a class of economies with collective ownership, sufficient ‘specialization’ in the endowment holdings of these economies gives rise to a non-empty core, so achieving social stability. It is shown, moreover, that reductions in income inequality are consistent with social stability, to the extent that these reductions preserve or increase ‘specialization’ in the economy. Finally, we show that our notion of specialization is not limited to the privatized sector of the economy. Even in economies in which there is no privately held property, sufficient specialization guarantees that the economy is socially stable.     

Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part

In this paper, we consider an exchange economy à la Shitovitz (Econometrica 41:467–501, 1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley, known as the Shapley window model. We analyze the relationship between the set of the Cournot–Nash allocations of the strategic market game and the Walras allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably infinite, any Cournot–Nash allocation of the game is not a Walras allocation of the underlying exchange economy. Accordingly, in the original spirit of Cournot (Recherches sur les principes mathématiques de la théorie des richesses. Hachette, Paris, 1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. Our main theorem shows that any sequence of Cournot–Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy.     

John von Neumann, the Mathematician

Imagine a poll to choose the best-known mathematician of the twentieth century. No doubt the winner would be John von Neumann. Reasons are seen, for instance, in the title of the excellent biography [M] by Macrae: John von Neumann. The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. Indeed, he was a fundamental figure not only in designing modern computers but also in defining their place in society and envisioning their potential. His minimax theorem, the first theorem of game theory, and later his equilibrium model of economy, essentially inaugurated the new science of mathematical economics. He played an important role in the development of the atomic bomb. However, behind all these, he was a brilliant mathematician. My goal here is to concentrate on his development and achievements as a mathematician and the evolution of his mathematical interests.