Euler Equation Errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross- sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard model's Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.

The periodic b-equation and Euler equations on the circle

In this note we show that the periodic b-equation can only be realized as an Euler equation on the Lie group Diff(S^1) of all smooth and orientiation preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm equation. In this case the inertia operator generating the metric on Diff(S^1) is given by A=1-d^2/dx^2. In contrast, the Degasperis-Procesi equation, for which b=3, is not an Euler equation on Diff(S^1) for any inertia operator. Our result generalizes a recent result of B. Kolev.Comment: 8 page

Financial integration in Europe: Evidence from Euler equation tests

This paper applies Obstfeld's Euler equation tests to assess the degree of financial integration in the European Union. In addition, we design a new Euler equation test which is intimately related to Obstfeld's Euler equation tests. Using data from the latest Penn World Table (Mark 6), we arrive at the following ranking of financial integration in the European Union: low integration (Greece and Portugal) intermediate (Austria, Denmark, Finland, France, Ireland, Italy, Spain and Sweden) and high (Belgium, Germany, the Netherlands and the United Kingdom). Furthermore, it appears that there is still significant room for risk diversification among European Union countries.EU;International Financial Markets;euler equations;Financial Integration;finance

Acoustic Limit for the Boltzmann equation in Optimal Scaling

Based on a recent $L^{2}{-}L^{\infty}$ framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions

Inviscid models generalizing the 2D Euler and the surface quasi-geostrophic equations

Any classical solution of the 2D incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This paper studies solutions of a family of active scalar equations in which each component $u_j$ of the velocity field $u$ is determined by the scalar $\theta$ through $u_j =\mathcal{R} \Lambda^{-1} P(\Lambda) \theta$ where $\mathcal{R}$ is a Riesz transform and $\Lambda=(-\Delta)^{1/2}$. The 2D Euler vorticity equation corresponds to the special case $P(\Lambda)=I$ while the SQG equation to the case $P(\Lambda) =\Lambda$. We develop tools to bound $\|\nabla u||_{L^\infty}$ for a general class of operators $P$ and establish the global regularity for the Loglog-Euler equation for which $P(\Lambda)= (\log(I+\log(I-\Delta)))^\gamma$ with $0\le \gamma\le 1$. In addition, a regularity criterion for the model corresponding to $P(\Lambda)=\Lambda^\beta$ with $0\le \beta\le 1$ is also obtained