Mixing on function spaces

Summary We prove that a probability measure over a space of functions induces a measure over the product space of the image and range of these functions. As an application, we show that the equilibrium of large anonymous games with uncertainty completely describes the behavior of players. In the second part of the paper we prove that mixed strategies over function spaces are equivalent to behavioral and distributional strategies.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

Public spending and optimal taxes without commitment

We consider a representative agent, infinite-horizon economy where production requires private and public capital. The supply of public capital is financed through distortionary taxation. The optimal (second best) tax policy of a benevolent government is time inconsistent. We therefore introduce explicitly the constraint that at no point in time the revision of the original tax plan is desirable. We completely characterize the (third best) tax plan that satisfies this constraint, and estimate the difference in tax rate between the second and third best policy for a wide range of parameters. For some of these the difference between the second and third best tax rates is large, and so are the associated rates of economic growth.     

The Relationship Between Saving and Credit from a Schumpeterian Perspective

After 1995, the United States experienced housing and mortgage booms, fuelled by increased lending from less regulated institutions, such as hedge funds. At the micro level, the housing boom may have left families with more wealth, but the mortgage boom may have increased their financial vulnerability. Using the Federal Reserve’s Survey of Consumer Finances, we consider both wealth creation and a select number of financial vulnerability measures of homeowners. The data indicate that the housing boom was not only associated with larger house values, but also moderated wealth gains and substantially greater financial vulnerability of homeowners. Both trends were more pronounced among middleincome and Hispanic families, who saw larger wealth gains, but also greater increases in financial vulnerability than their counterparts. Given the breadth of the spread in homeowners’ financial vulnerability alongside sharply higher house prices, our results support the link between more deregulated financial markets and rising financial instability.     

Optimal Portfolio Selection Based on Expected Shortfall Under Generalized Hyperbolic Distribution

This paper discusses optimal portfolio selection problems under Expected Shortfall as the risk measure. We employ multivariate Generalized Hyperbolic distribution as the joint distribution for the risk factors of underlying portfolio assets, which include stocks, currencies and bonds. Working under this distribution, we find the optimal portfolio strategy.     

Trasformata inversa di laplace per funzioni positive e problema dei momenti

Si propone un nuovo metodo per l'inversione numerica della transformata di Laplace per funzioni positive, tipicamente densità di probabilità. La funzione approssimante è ottenuta ricorrendo al principio di Massima Entropia, assumendo come informazione limitata i momenti della funzione da ricostruire, a loro volta legati da ben note relazioni alle derivate della funzione transformata. Dopo aver richiamato alcuni risultati teorici noti in letteratura concernenti l'esistenza dell'approssimante e la convergenza in entropia (e di conseguenza in normaL ₁), si presentano alcuni risultati teorici originali sul condizionamento del problema e alcuni risultati numerici che illustrano la bontà dell'approssimante.

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Summary A new method for the numerical Laplace transform inversion of positive functions, tipically probability density functions, is proposed. The approximating function is obtained resorting to the maxientropic approach, by assuming its moments as partial available information. Some known theoretical results concerning the existence and entropy convergence are reviewed. New theoretical results about the conditioning of the problem and some numerical simulations are illustrated.

     

Intertemporal pricing in laboratory posted offer markets with differential information

Summary. This paper analyzes intertemporal seller pricing and buyer purchasing behavior in a laboratory retail market with differential information. A seller posts one price each period that a buyer either accepts or rejects. Trade occurs over a sequence of "market periods" with a random termination date. The buyer and seller are differentially informed: The seller's cost of producing a unit of a fictitious good is known and constant in all periods, but the buyer's value for the good (demand) is a random variable governed by a Markov Process whose structure is common knowledge. At the beginning of each period the unit's value is determined by "nature" and is privately revealed only to the buyer. The market termination rule is a binary random variable. We conduct 32 laboratory experiments designed to study intertemporal pricing by human subjects in the Posted Offer Institution when demand follows a stochastic process. There are four series of experiments: 8 with simulated buyers, 8 with inexperienced subjects, 8 with once experienced subjects, and 8 with twice experienced subjects.     

The Design and Performance of Sharing Rules for a Partnership in Continuous Time

We study repeated partnerships with imperfect monitoring and risk neutrality. The interval between the partners' decisions, the delay, is given but can be arbitrarily small. Each stage-game's output is Gaussian, with mean and variance depending on the partners' actions, making the sequence of outcomes a discretization of a diffusion. A sharing rule is efficient if there is an equilibrium of the corresponding game whose outcomes are Pareto efficient; it is stable if these equilibria approach a limit as the delay approaches zero. We characterize partnerships for which there exist stable, efficient sharing rules, and describe the corresponding equilibria.Journal of Economic LiteratureClassification Numbers: C73, D2, D82.     

Problemi di classificazione e connessione in una classe di grafi planari a facce esagonali

Aldo Ruscitti è mancato a Roma il 20 agosto 1978 a soli 39 anni di età. Era stato assistente ordinario e professore incaricato di Istituzioni di Analisi Matematica nella Facoltà di Scienze Statistiche Demografiche e Attuariali dell’Università di Roma. Sin dalla preparazione della tesi di laurea, i suoi interessi scientifici erano stati rivolti alle applicazioni della matematica in campo economico. Nell’ultimo periodo della sua attività si era impegnato in ricerche sulla struttura di particolari classi di grafi, settore nel quale aveva conseguito risultati a livello internazionale. Con la pubblicazione postuma di questo contributo di A. Ruscitti intendiamo rendere un affettuoso omaggio alla memoria di un caro amico che tra i primi aveva voluto entrare a far parte della famiglia dell’AMASES.

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On the problems of classification and enumeration in a class of 6-valent planar graphs

In this article the author investigates the problems of classification and enumeration of maps with the vertices of degree six and with the faces of cardinality two or three. The graphs in this class are analysed in terms of the maximal number of vertices with degree two they possess on the boundary of their faces. Special emphasis is placed on the problem of the connectivity of these graphs, according with the suggestion of B. Grünbaum and J. Zaks (see [4], p. 112): in particular the author proves that there exist 5-connected graphsG _n in this class with degreen> , for all εN.