On homogeneous warped product Einstein metrics

In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous $(\lambda,n+m)$-Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a question from a paper of C. He, P. Petersen and W. Wylie, where they prove the converse statement. Our proof is strongly based on their results, but it also makes use of sharp tools from the theory of homogeneous Ricci solitons. As an application, we obtain that any homogeneous warped product Einstein metric with homogeneous base is diffeomorphic to a product of homogeneous Einstein manifolds.Comment: 9 page

Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat

Phase behavior of hard-core lattice gases: A Fundamental Measure approach

We use an extension of fundamental measure theory to lattice hard-core fluids to study the phase diagram of two different systems. First, two-dimensional parallel hard squares with edge-length $\sigma=2$ in a simple square lattice. This system is equivalent to the lattice gas with first and second neighbor exclusion in the same lattice, and has the peculiarity that its close packing is degenerated (the system orders in sliding columns). A comparison with other theories is discussed. Second, a three-dimensional binary mixture of parallel hard cubes with $\sigma_{\rm{L}}=6$ and $\sigma_{\rm{S}}=2$. Previous simulations of this model only focused on fluid phases. Thanks to the simplicity introduced by the discrete nature of the lattice we have been able to map out the complete phase diagram (both uniform and nonuniform phases) through a free minimization of the free energy functional, so the structure of the ordered phases is obtained as a result. A zoo of entropy-driven phase transitions is found: one-, two- and three-dimensional positional ordering, as well as fluid-ordered phase and solid-solid demixings.Comment: 14 pages, 16 figure

THE BIAS FOR FORWARD EXCHANGE RATE AND THE RISK PREMIUM: AN EXPLANATION WITH A STOCHASTIC AND DYNAMIC GENERAL EQUILIBRIUM MODEL

Forward exchange rate unbiassedness is rejected in test for international exchange markets. Such issue can be interpreted as evidence of a biased forward rate and/or time-varying risk premia. This paper proposes a stochastic general equilibrium model which generates substantial variability in the magnitude of predictable excess returns. Simulation exercises suggest that higher persistency in the monetary policy produces higher bias in the estimated slope coefficient in the regression of the change in the logarithm of the spot exchange rate on the forward premium. Also, our model suggest that the nature of the transmission between monetary shocks can explain the excess returns puzzle. Empirical evidence for the DM-USD rate that support our theoretical results is provided. La insesgadez del tipo forward ha sido ampliamente rechazada en los estudios empíricos sobre los mercados de tipo cambio internacionales. Este aspecto puede interpretarse como la existencia de un sesgo en la capacidad predictiva del tipo forward y/o la presencia de una prima de riesgo cambiante en el tiempo. Este trabajo propone un modelo dinámico y estocástico de equilibrio general que genera amplia volatilidad en la prima de riesgo. Los ejercicios de simulación llevados a cabo sugieren que una mayor persistencia de la política monetaria produce un mayor sesgo en la pendiente estimada de una regresión del cambio en el logaritmo del tipo spot sobre la prima de riesgo. Además, el modelo sugiere que la naturaleza de la transmisión de los shocks monetarios puede explicar dicho sesgo. Finalmente, el trabajo presenta evidencia empírica sobre el tipo de cambio entre el marco alemán y el dólar americano en línea con los resultados teóricos.Teoría de las expectativas, Prima de riesgo, Tipo de cambio forward, Simulación. Expectations theory, Risk premium, Forward exchange rates, Simulations.

THE EFFECT OF THE EMU ON SHORT AND LONG-RUN STOCK MARKET DYNAMICS: NEW EVIDENCE ON FINANCIAL INTEGRATION

This paper deals with the time evolution of stock market integration around the introductionof the euro. In particular we test whether the degree of integration between the main eurozonecountries increased after European monetary union. The contribution of the paper to the extantliterature is twofold: a) first, we take into account the potential long-run equilibrium relationshipbetween stock indices allowing for structural changes in the cointegration space that might capturethe effect of the introduction of the euro, and b) we formally test the existence of greater financialintegration after European monetary union across the main member countries and between thesemembers and the UK. Empirical evidence reveal the existence of long-run equilibrium relationshipsbetween European stock markets even before the introduction of the euro. Our empirical findingssuggest that financial integration is not the direct consequence of the removal of exchange rate riskdue to currency unification. Rather, it arises as a result of macroeconomic convergence. This aspectis corroborated by the nature of the principal component structure of estimated conditionalcorrelations. Este trabajo analiza la evolución del grado de integración de los mercados bursátileseuropeos en torno a la introducción del euro. En particular se contrasta si el grado de integraciónentre los principales miembros de la Unión Europea y Monetaria se ha incrementado a partir de laintroducción del euro. La contribución del trabajo es doble: a) por un lado se tiene en cuenta laposible existencia de relaciones de cointegración entre los índices bursátiles, permitiendo laexistencia de cambios estructurales en el espacio de cointegración y b) se proporciona un contrasteformal para la hipótesis nula de mayor grado de integración después de la introducción de la monedacomún. La evidencia empírica revela la existencia de relaciones de equilibrio a largo plazo entre losmercados, incluso antes de la introducción del euro. Los resultados sugieren que la integraciónfinanciera no es el resultado de la adopción de la moneda común sino que es un proceso dinámicoque se ha visto fortalecido por la unificación de la moneda. Este aspecto es corroborado por lanaturaleza de la estructura de componentes principales que se obtiene a partir de la medida deintegración considerada.cointegración, mercados financieros, Unión Europea y Monetaria, integración financiera dinámica cointegration, dynamic financial integration, stock markets, European Monetary Union.