Excess demand function around critical prices in incomplete markets

We show that the aggregate excess demand function in an economy with incomplete real asset markets can be characterized by Walras’ law, homogeneity, and continuity around critical prices that cause one-dimensional drop of the dimension of the budget set.     

Slack in incomplete markets with nominal assets: A symmetric proof

In this paper, we provide an equilibrium analysis in the framework of incomplete markets where some agents’ preferences are possibly satiated at some state of the nature. We will consider nominal assets with exogenously fixed asset prices. We extend the notion of equilibrium with slack – introduced by Drèze and Müller [Drèze, J., Müller, H., 1980. Optimality properties of rationing schemes. Journal of Economic Theory 23, 150–159] in a fixed price setting – to the GEI framework.     

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.     

Minimax price bounds in incomplete markets

This paper develops an approach to tighten the bounds on asset prices in an incomplete market by combining no-arbitrage pricing and preference-based pricing, and the approach is applied to a call option in the absence of dynamic rebalancing. With the no-arbitrage pricing, it is straightforward to obtain the initial bounds, which are too wide to be of practical uses. By accepting that a representative agent exhibits risk aversion from a benchmark pricing kernel, it is possible to narrow the bounds considerably. Using the unbiased minimax deviation implicit in the parameters, one can restrict further the set of reasonable values on assets in incomplete markets.     

Taxes and money in incomplete financial markets

Abstract We analyze a model with incomplete financial markets, where money is needed to pay taxes. Equilibria exist, are typically regular and not Pareto optimal. Moreover, generically, there exists a redistribution of money among households which leads to a Pareto superior equilibrium. The intervention occurs only in the first period and it does not require either closing markets or upper bounds on the number of households. Mathematics Subject Classification (2000): 91B50 Journal of Economic Literature Classification: D52, D60, E50, H20     

Production in incomplete markets: Expectations matter for political stability

In the present paper we study voting-based corporate control in a general equilibrium model with incomplete financial markets. Since voting takes place in a multi-dimensional setting, super-majority rules are needed to ensure existence of equilibrium. In a linear–quadratic setup we show that the endogenization of voting weights (given by portfolio holdings) can give rise to – through self-fulfilling expectations – dramatical political instability, i.e. Condorcet cycles of length two even for very high majority rules.     

Vertical syndication-proof competitive prices in multilateral assignment markets

We consider a market comprising a number of perfectly complementary and homogeneous commodities. We concentrate on the incentives for firms producing these commodities to merge and form a vertical syndicate. The main result establishes that the nucleolus of the associated market game corresponds to the unique vector of prices with the following properties: (i) they are vertical syndication-proof, (ii) they are competitive, (iii) they yield the average of the buyers- and the sellers-optimal allocations in bilateral markets, and (iv) they depend on the traders’ bargaining power but not on their identity. The proof uses an isomorphism between our class of market games and the entire class of bankruptcy games.     

Notes on pareto improvement in incomplete financial markets

these notes describe some recent developments in the analysis of the possibilities for Pareto improvement when, in a competitive environment, financial markets are incomplete. The basic framework is a general methodology for investigating the welfare effects of policy or institutional changes in equilibrium models, when these can be characterized in terms of perturbing the solutions to a system, of smooth equations. Two particular scenarios are discussed in detail: First, the situation where a central government can intervene in the form of wealth taxes and subsidies, and second, the situation where the financial institutions can be modified by increasing the number of available instruments.

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Sommario Queste osservazioni descrivono alcuni sviluppi recenti dell'analisi del miglioramento paretiano quando, in un contesto competitivo, i mercati finanziari sono incompleti. La struttura di riferimento è la metodologia generale per indagare gli effetti sul benessere sociale di cambiamenti politici o istituzionali nei modelli di equilibrio, quando questi possono essere caratterizzati come una perturbazione delle soluzioni di un sistema di equazioni. Due scenari particolari vengono discussi in dettaglio: nel primo, un governo centrale può intervenire attraverso la tassazione sulla ricchezza e le sovvenzioni; nel secondo, le istituzioni finanziarie possono essere modificate mediante l'aumento degli strumenti disponibili.

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While working in this general area I have benefitted substantially from interaction and collaboration with several of my, sometime Penn colleagues or students, Alex Citanna, Atsushi Kajii, Marcos Lisboa and Antonio Villanacci. Conversations at various points with Ronel Elul, John Geanakoplos, Heracles Polemarchakis and especially, Paolo Siconolfi have also been extremely helpful and illuminating. None of them, however, is responsible for my biases and idiosyncrasies. These notes were prepared for a presentation at the AMASES Conference held in Pugnochiuso, Italy during September 25–28, 1995.     

Drivers of optimal prices in two-sided markets: the state of the art

In two-sided markets, a platform has two groups of customers and enables their interactions. Demand on one market side depends on demand on the other; therefore, when platforms set prices, they must consider this interdependency and set prices on both sides simultaneously. By surveying the vast theoretical marketing and economics literature, this article provides a clear and systematic overview of profit-maximizing pricing in two-sided markets. It identifies and structures the various drivers of those optimal prices. Using this framework, it summarizes the findings from prior research and offers an assessment of the state of the art with regard to drivers of optimal prices and their impacts on a platform’s price setting. This improves understanding of both the principles of two-sided markets and their optimal pricing. Finally, this state of the art paper suggests some directions for further research.     

Solving the incomplete markets model with aggregate uncertainty by backward induction

This paper describes a method to solve models with a continuum of agents, incomplete markets and aggregate uncertainty. I use backward induction on a finite grid of points in the aggregate state space. The aggregate state includes a small number of statistics (moments) of the cross-sectional distribution of capital. For any given set of moments, agents use a specific cross-sectional distribution, called “proxy distribution”, to compute the equilibrium. Information from the steady state distribution as well as from simulations can be used to chose a suitable proxy distribution.     

Shadow costs of incomplete information and short sales in the valuation of the firm and its assets

This paper presents a simple framework for the valuation of compound options within shadow costs of incomplete information and short sales. The shadow cost includes two components. The first component is the product of pure information cost due to imperfect knowledge and heterogeneous expectations. The second component represents the additional cost caused by the short-selling constraint. Information costs are linked to Merton's (1987. Journal of Finance 42, 510) model of capital market equilibrium with incomplete information, CAPMI. This model is extended by Wu et al. (1996. Review of Quantitative Finance and Accounting, 7, 136) who propose an incomplete-information capital market equilibrium with heterogeneous expectations and short sale restrictions, GCAPM. This model is used in our paper to provide for the first time in the literature analytic solutions for derivatives in the presence of both shadow costs of incomplete information and short sales.When deriving the compound call option formula, we consider a call option on a stock, which is itself an option on the assets of the firm. Our methodology incorporates shadow costs of incomplete information and short sales on the firm's assets as well as the effects of leverage in the capital structure. The formula can be useful in the valuation of several corporate liabilities in the presence of information uncertainty and short sales constraints about the firm and its cash flows. Our analysis can be used for the valuation of several real options.     

Equilibrium in incomplete markets: I : A basic model of generic existence

This paper demonstrates the generic existence of general equilibria in incomplete markets. Our economy is a model of two periods, with uncertainty over the state of nature to be revealed in the second period. Securities are claims to commodity bundles in the second period that are contingent on the state of nature, and are insufficient in number to span all state contingent claims to value, regardless of the announced spot commodity prices. Under smooth preference assumptions, equilibria exist except for an exceptional set of endowments and securities, a closed set of measure zero. The paper includes partial results for fixed securities, showing the existence of equilibria except for an exceptional set of endowments.     

2007年第一季度 城市地价动态监测报告

根据中国城市地价动态监测系统对全国重点地区和主要城市监测结果的分析，2007年第一季度我国主要城市地价状况如下——     

Bounds for the median of the negative binomial distribution

Summary Bounds are obtained for the median of the negative binomial distribution which are valid for all possible parameter values of the distribution when the median is defined as inf {x: P(X≤x)≥1/2}.     

Bounds for the variance of an inverse binomial estimator

Summary  B est [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. M ikulski and Sm [2] gave an upper bound to it, easier to calculate than B est's expression and a good approximation for small values of p and large values of r (the number of successes). In this paper both lower bounds and closer upper bounds are derived.     

General equilibrium in markets for lemons

This paper studies exchange economies in which agents have differential information about the goods that the other agents bring to the market. To study such a setting, it is useful to distinguish goods not only by their physical characteristics, but also by the agent that brings them to the market. Equilibrium is shown to exist, with agents receiving the cheapest bundle among those that they cannot distinguish from the truthful delivery. An example is presented as an illustration.     

Bounds for best response functions in binary games

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment-response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment-response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.