Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.     

Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L_∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.As for our existence result, we consider the framework of Bewley (1972). However, there are four major problems in using this technique. To overcome two of these difficulties, we impose strong lower hemi-continuity assumptions upon the economies. The remaining problems are removed when the finite economies are large enough.Our model encompasses previous works on the existence of general equilibria when there are externalities and non-convexities but the commodity space is finite dimensional and those on general equilibria in non-convex economies with infinitely many commodities when no external effect is taken into account.     

A note on strategies for bandit problems with infinitely many arms

A bandit problem consisting of a sequence of n choices (n) from a number of infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution F on the interval [0,1] and F is continuous with F(0)=0 and F(1)=1. The goal is to investigate the asymptotic expected failure rates of k-failure strategies, and obtain a lower bound for the expected failure proportion over all strategies presented in Berry et al. (1997). We show that the asymptotic expected failure rates of k-failure strategies when 0<b1 and a lower bound can be evaluated if the limit of the ratio F(1)–F(t) versus (1–t)^b exists as t1^– for some b>0.     

A remark on the existence of equilibria in markets without ordered preferences and with a Riesz space of commodities

We show the existence of competitive equilibria in economies without ordered preferences and a Hausdorff locally convex solid Riesz space of commodities. Our principal assumptions are that the commodity space has a predual and that its positive cone has a non-empty interior.     

Some results on the weak core of a non-side-payment game with infinitely many players

The present note considers a balanced game without side payments with a continuum of players. A concept of weak core for such games is introduced. Then a non-emptiness theorem for the weak core is proved for a class of games.     

Existence, uniqueness and determinacy of Arrow–Debreu equilibria in finance models

We characterize the Arrow–Debreu equilibria of a pure exchange one good economy where agents have additively separable utilities. It is then shown that under gross substitution hypotheses on utilities (or if relative risk aversion is smaller than one), the excess utility has gross substitute properties. Uniqueness of equilibria thus follows. It is finally proved that generically equilibria are determinate.     

Core equivalence theorem: countably many types of agents and commodities in $\vec{L}^{1}(\mu)$

Abstract  We prove a core-Walras equivalence result for a finitely additive confederate economy with commodity space L¹(μ) and a measurable bounded map of extremely desirable commodities: when the map of extremely desirable commodities is simply bounded the properness of preferences is no longer equivalent to the existence of just one extremely desirable commodity as assumed in the countably additive model by Rustichini and Yannelis. Mathematics Subject Classification: 91B50, 91B54; 28B20, 46A22, 28A25 Journal of Economic Literature Classification: D51; C02     

A note on computing equilibria in economies with activity analysis models of production

Equilibria in economies without production can be approximated by computing fixed points of continuous functions. With production present, the functions are usually replaced by set-valued mappings and fixed-point algorithms converge slowly. Here we propose continuous functions whose fixed points are equilibria in economies whose production is modelled by a finite list of activities. The penalty is that a least-distance program must be solved at each iteraction. The approach generalizes to allow ad valorem taxes on production. Finally, analogous arguments apply to the computation of an invariant optimal vector of capital stocks.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

Existence of financial equilibria with endogenous short selling restrictions and real assets

We consider a model with real assets and restricted participation described by household-specific price-dependent short selling constraints. We show existence of equilibria for all elements in an explicitly characterized large subset of the set of economies.     

Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.     

论湖南省旅游商品与湖湘文化的融合开发

文章以湖南为例,从文化视角探讨湖湘文化与旅游商品开发的融合基础,提出建立湖湘文化———湖南旅游形象———湖南旅游商品的系统思维链,以便能积极推进旅游商品和旅游业的快速稳健发展。     

A remark on rational expectation equilibria with incomplete markets and real assets

In this note, I established the existence, for a generic set of endowments, of a fully revealing rational expectation equilibrium (REE) in an economy characterized by incomplete markets and real assets.     

Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional value-at-risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal approximation method and the data tilting method, for constructing confidence intervals for the conditional VaR estimator and assess their accuracies by simulation studies. Finally, we apply the proposed approach to an energy market data set.     

Equilibrium models with land: A criticism and an alternative

Models of economies either of urban areas or with local public goods often involve the use of a continuum of consumers along with the use of a commodity called land; each consumer generally owns a parcel of land of positive area. The purpose of the present study is to show that such models are internally inconsistent (independent of the other assumptions employed) in that only countably many consumers can own parcels of land of non-zero area if land lies in a Euclidean space. This result applies, in particular, to monocentric city models. Moreover, it is shown that the standard justification for the use of economies with an infinity of agents, that they approximate large economies with a finite number of consumers, does not necessarily apply in the case of economies with land and a continuum of consumers. A model where land is represented by subsets of $\text{R}$² is presented as an alternative.     

Default models based on scale mixtures of Marshall-Olkin copulas: properties and applications

We present a unification of the Archimedean and the Lévy-frailty copula model for portfolio default models. The new default model exhibits a copula known as scale mixture of Marshall-Olkin copulas and an investigation of the dependence structure reveals that desirable properties of both original models are combined. This allows for a wider range of dependence patterns, while the analytical tractability is retained. Furthermore, simultaneous defaults and default clustering are incorporated. In addition, a hierarchical extension is presented which allows for a heterogeneous dependence structure. Finally, the model is applied to the pricing of CDO contracts. For this purpose, an efficient Laplace transform inversion approach is developed. Supporting a separation of marginal default probabilities and dependence structure, the model can be calibrated to CDS contracts in a first step. In a second step, the calibration of several parametric families to CDO contracts demonstrates a good fitting quality, which further emphasizes the suitability of the approach.