Ergodicity, Decisions, and Partial Information

In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that one may choose (under a mild integrability assumption) a decision strategy whose pathwise time-average loss is asymptotically smaller than that of any other strategy. The corresponding problem in the case of partial information proves to be much more delicate, however: if the process X is not observable, but decisions must be based on the observation of a different process Y, the existence of pathwise optimal strategies is not guaranteed. The aim of this paper is to exhibit connections between pathwise optimal strategies and notions from ergodic theory. The sequential decision problem is developed in the general setting of an ergodic dynamical system (\Omega,B,P,T) with partial information Y\subseteq B. The existence of pathwise optimal strategies grounded in two basic properties: the conditional ergodic theory of the dynamical system, and the complexity of the loss function. When the loss function is not too complex, a general sufficient condition for the existence of pathwise optimal strategies is that the dynamical system is a conditional K-automorphism relative to the past observations \bigvee_n T^n Y. If the conditional ergodicity assumption is strengthened, the complexity assumption can be weakened. Several examples demonstrate the interplay between complexity and ergodicity, which does not arise in the case of full information. Our results also yield a decision-theoretic characterization of weak mixing in ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page

Information frictions and adverse selection: policyinterventions in health insurance markets

This paper develops and implements a general framework to study insurance market equilibrium and evaluate policy interventions in the presence of choice frictions. Friction-reducing policies can increase welfare by facilitating better matches between consumers and plans, but can decrease welfare by increasing the correlation between willingness-to-pay and costs, exacerbating adverse selection. We identify relationships between the underlying distributions of consumer (i) costs (ii) surplus from risk protection and (iii) choice frictions that determine whether friction-reducing policies will be on net welfare increasing or reducing. We extend the analysis to study how policies to improve consumer choices interact with the supply-side policy of risk-adjustment transfers and show that the effectiveness of the latter policy can have important implications for the effectiveness of the former. We implement the model empirically using proprietary data on insurance choices, utilization, and consumer information from a large firm. We leverage structural estimates from prior work with these data and highlight how the model's micro-foundations can be estimated in practice. In our specific setting, we find that friction-reducing policies exacerbate adverse selection, essentially leading to the market fully unravelling, and reduce welfare. Risk-adjustment transfers are complementary, substantially mitigating the negative impact of friction-reducing policies, but having little effect in their absence

Spatiotemporal complexity of the universe at subhorizon scales

This is a short note on the spatiotemporal complexity of the dynamical state(s) of the universe at subhorizon scales (up to 300 Mpc). There are reasons, based mainly on infrared radiative divergences, to believe that one can encounter a flicker noise in the time domain, while in the space domain, the scaling laws are reflected in the (multi)fractal distribution of galaxies and their clusters. There exist recent suggestions on a unifying treatment of these two aspects within the concept of spatiotemporal complexity of dynamical systems driven out of equilibrium. Spatiotemporal complexity of the subhorizon dynamical state(s) of the universe is a conceptually nice idea and may lead to progress in our understanding of the material structures at large scalesComment: references update

The social determinants of choice quality: evidence from health insurance in the Netherlands

Market provision of impure public goods such as insurance, retirement savings and education is common and growing as policy makers seek to offer more choice and gain efficiencies. This approach induces an important trade-off between improved surplus from matching individuals to products and misallocation due to well documented choice errors in these markets. We study this trade-off in the health insurance market in the Netherlands, with a specific focus on misallocation and inequality. We characterize choice quality as a function of predicted health risk and leverage rich administrative data to study how it depends on individual human capital, socioeconomic status and social and information networks. We find that choice quality is low on average, with many people foregoing options that deliver substantive value. We also find a strong choice quality gradient with respect to key socioeconomic variables. Individuals with higher education levels and more analytic degrees or professions make markedly better decisions. Social influence on choices further increases inequality in decision making. Using panel variation in exposure to peers we find strong within firm, location and family impacts on choice quality. Finally, we use our estimates to model the consumer surplus effects of different counterfactual scenarios. While smart default policies could improve welfare substantially, including the choice of a high-deductible option delivers little welfare gain, especially for low-income individuals who make lower quality choices and are in worse health

Spectral theory for the failure of linear control in a nonlinear stochastic system

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems the nonnormality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the nonnormality and the type of nonlinearity are all crucially important to understanding and describing the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong nonnormality is due to the presence of mean flow rather than the action of control.Comment: Submitted to Physical Review

Eigenschwingungsanalyse an der Seitenwand einer Verarbeitungsmaschine

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Michele Taruffo and collectives process in Latin America

A través de revisión bibliográfica, así como de legislaciones y anteproyectos, este trabajo trata de los aportes de Michele Taruffo con respecto a la tutela colectiva. Teniendo como problema de investigación si existe en la materia un legado de Michele Taruffo para la América Latina, este estudio tomó como referencia el Código Modelo de Procesos Colectivos para Iberoamérica para verificar la influencia de las ideas del maestro italiano, sea en la ordenación del antedicho anteproyecto, sea en la adopción de soluciones propuestas por él. Al final de la pesquisa, además de la difusión de los métodos de investigación orientados a la solución de problemas prácticos, se puede concluir que el gran profesor lombardo fue muy importante para el principio y la conformación de la tutela colectiva de Latinoamérica.Through bibliographic review, as well as legislations and bills, this work addresses the contribution of Michele Taruffo about the collective process. Having as research problem if there was a legacy of the Italian jurist for Latin America in the matter, this study took as a reference the Model Class Action Code for Ibero-America to verify if there was influence of the ideas of Michele Taruffo, either in the conformation of the aforementioned draft, or in the adoption of the solutions proposed by him. At the end of the survey, in addition to the dissemination of research methods aimed at solving practical problems, it can be concluded that the great Lombard professor was very important for the beginning and formation of the class action in Latin America.Facultad de Ciencias Jurídicas y Sociale

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page

Pathogenic Potential to Humans of Bovine Escherichia coli O26, Scotland

Escherichia coli O26 and O157 have similar overall prevalences in cattle in Scotland, but in humans, Shiga toxin–producing E. coli O26 infections are fewer and clinically less severe than E. coli O157 infections. To investigate this discrepancy, we genotyped E. coli O26 isolates from cattle and humans in Scotland and continental Europe. The genetic background of some strains from Scotland was closely related to that of strains causing severe infections in Europe. Nonmetric multidimensional scaling found an association between hemolytic uremic syndrome (HUS) and multilocus sequence type 21 strains and confirmed the role of stx<sub>2</sub> in severe human disease. Although the prevalences of E. coli O26 and O157 on cattle farms in Scotland are equivalent, prevalence of more virulent strains is low, reducing human infection risk. However, new data on E. coli O26–associated HUS in humans highlight the need for surveillance of non-O157 enterohemorrhagic E. coli and for understanding stx<sub>2</sub> phage acquisition

A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42