Unique solutions for stochastic recursive utilities

We study unique and globally attracting solutions of a general nonlinear stochastic equation, widely used in Finance and Macroeconomics and closely related to stochastic Koopmans equations. The equation is specified by a temporal aggregator W and a certainty equivalent operator M. The main contribution of the paper is the introduction of the new class of Thompson aggregators. Other contributions of the paper are: (i) a detailed analysis of quasi-arithmetic operators M that generalize those of Kreps and Porteus (1978) [18]; (ii) a clarification of the nature and properties of the stochastic recursive preferences that underlie Koopmans equations.     

Global Rebalancing and the Future of the Sino-US Codependency

The crisis of 2008 has shown the unsustainability of the global imbalances centered on the US-China symbiotic relationship that characterized the previous decade. This has revived the so-called growth-rebalancing debate. In particular, the new emerging consensus calls for a re-orientation of the US economy away from consumption and toward exports, and for policy shifts that can help China to reduce its dependence on external demandand inefficiently high rates of capital accumulation. We discuss the economic and political feasibility of the proposed patterns of re-adjustment by focusing on the short-term and long-term trade-offs faced by the policy-makers. We argue that the rebalancing will be gradual and partial because of the costs associated with a radical shift in the growth models adopted by both countries. We believe that this scenario will be consistent with a world economy expanding at lower rates than over the past decade.     

Un modello non lineare sul funzionamento dei mercati azionari

Si analizza il funzionamento di un mercato azionario dove gli agenti sono caratterizzati da razionalità limitata, comportamento eterogeneo e disponibilità limitata di risorse finanziarie. La dinamica del mercato azionario viene spiegata attraverso un sistema non lineare del secondo ordine, a tempo continuo. Vengono esaminate le biforcazioni verificantesi al variare di un parametro avente particolare significato dal punto di vista finanziario. Ciò consente di rilevare l'esistenza di diverse modalità di funzionamento asintotico. Come suggerito dall'intuizione, al crescere del numero degli agenti dotati di minore razionalità, la dinamica del mercato diviene sempre più irregolare.

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Summary A stock market model is conceived within which investors are qualified by bounded rationality, asymmetric behaviour, and restricted availability of money. The stock market is represented through a second order nonlinear model which is continuous in time. Attention is attached to the bifurcations that arise when a financially meaningful parameter is suitably varied. In this way a range of asymptotic behaviours is detected. As one would expect, an excess in traders with low rationality results in an unstable market.

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Si ringraziano sentitamente il Prof. S. Baldone, il Prof. M. Gatto, il Dott. M. Miari, il Prof. L. Peccati ed il Prof. S. Rinaldi per i preziosi suggerimenti offerti.     

Firm Size Distribution in Small Samples

Sutton (1998) has recently proposed a theoretical lower bound to firm size inequality when a market is made of several independent submarkets. His results are valid asymptotically, as the number of submarkets becomes arbitrarily large. We show that, in small samples, his results can be interpreted as a positive relationship between an index of firm size inequality and the number of submarkets. We also test this relationship in the Italian motor insurance market.     

A new turnpike theorem for discounted programs

Summary In this paper we present new results on the local and global convergence property of solutions to an optimization model where the objective function is a discounted sum of stationary one-period utilities. The asymptotic local turnpike is given without differentiability assumptions but imposing some mild curvature restrictions on the utility function. This approach allows us to get easy estimates on the range of discount factors and the size of the neighborhood for which the asymptotic property occurs. The paper concludes by providing two global turnpike theorems. The first one is an asymptotic theorem derived from a result similar to Scheinkman's visit lemma. The second one turns out to be a restatement of McKenzie's neighborhood turnpike theorem.This research was partially supported by MURST, National Group on Nonlinear Dynamics in Economics and Social Sciences.     

Background Uncertainty and the Demand for Insurance Against Insurable Risks

Theory suggests that people facing higher uninsurable background risk buy more insurance against other risks that are insurable. This proposition is supported by Italian cross-sectional data. It is shown that the probability of purchasing casualty insurance increases with earnings uncertainty. This finding is consistent with consumer preferences being characterized by decreasing absolute prudence.     

The arrival of the new

In this work we present a number of urn models in which, contrary to standard Pólya urns, the number of competing alternatives is not given from the outset but may increase with the arrival of innovations. We begin by describing a variant of Pólya urns, first introduced by Fred Hoppe, in which balls of previously non-existing colors are added with some (declining) probability. We then propose new variants in which the probability of the arrival of new colors is itself subject to adaptive change depending on the success of past innovations and discuss applications to evolutionary models of technologies and industries. We numerically simulate different specifications of these urns with adaptively changing mutation rate and show that they can account for complex patterns of evolution in which periods of exploration and innovation are followed by periods in which the dynamics of the system is driven by selection among a stable set of alternatives.     

A note on the symmetry of all Nash equilibria in games with increasing best replies

It is well known that a symmetric game has only symmetric (pure strategy) Nash equilibria if its best-reply correspondences admit only increasing selections and its strategy sets are totally ordered. Several nonexamples of the literature show that this result is generally false when the totality condition of the relation that orders the strategy sets is simply dropped. Making use of the structure of interaction functions, this note provides sufficient conditions for the symmetry of all (pure strategy) Nash equilibria in symmetric games where best-reply correspondences admit only increasing selections, but strategy sets are not necessarily totally ordered.