Comparative Risk Aversion: A Formal Approach with Applications to Saving Behaviors

We consider a formal approach to comparative risk aversion and applies it to intertemporal choice models. This allows us to ask whether standard classes of utility functions, such as those inspired by Kihlstrom and Mirman [15], Selden [26], Epstein and Zin [9] and Quiggin [24] are well-ordered in terms of risk aversion. Moreover, opting for this model-free approach allows us to establish new general results on the impact of risk aversion on savings behaviors. In particular, we show that risk aversion enhances precautionary savings, clarifying the link that exists between the notions of prudence and risk aversion.Risk aversion, Savings behaviors, Precautionary savings

Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length

We extend previous work on applying the epsilon-expansion to universal properties of a cold, dilute Fermi gas in the unitary regime of infinite scattering length. We compute the ratio xi = mu/epsilon_F of chemical potential to ideal gas Fermi energy to next-to-next-to-leading order (NNLO) in epsilon=4-d, where d is the number of spatial dimensions. We also explore the nature of corrections from the order after NNLO.Comment: 28 pages, 14 figure

Correlation functions and dissipation in hot QCD

A recently proposed generating functional allows the construction of the full set of n-point Green functions in QCD at high temperature and at distances larger than 1/gT. One may then learn how the system maintains its thermal equilibrium in the quantum field theory approach, i.e. which process compensates for the important dissipation due to collisions. This system may be characterized by quantities which have a classical limit. One finds that the fluctuations of the coloured field are not gaussian ones. A comparison is made with the semi-classical approach where a random noise is the source of fluctuations.Comment: 21 pages, latex 2e, no figure Comments added in Introduction, in Sec

Mixed finite elements for numerical weather prediction

We show how two-dimensional mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo-uniform grids. This family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal C-grid finite difference methods. There are a few major advantages: the mixed finite element methods do not require an orthogonal grid, and they allow a degree of flexibility that can be exploited to ensure an appropriate ratio between the velocity and pressure degrees of freedom so as to avoid spurious mode branches in the numerical dispersion relation. These methods preserve several properties of the C-grid method when applied to linear barotropic wave propagation, namely: a) energy conservation, b) mass conservation, c) no spurious pressure modes, and d) steady geostrophic modes on the $f$-plane. We explain how these properties are preserved, and describe two examples that can be used on pseudo-uniform grids: the recently-developed modified RT0-Q0 element pair on quadrilaterals and the BDFM1-\pdg element pair on triangles. All of these mixed finite element methods have an exact 2:1 ratio of velocity degrees of freedom to pressure degrees of freedom. Finally we illustrate the properties with some numerical examples.Comment: Revision after referee comment

A generating functional for ultrasoft amplitudes in hot QCD

The effective amplitudes for gluon momentum p<<gT in hot QCD exhibit damping as a result of collisions. The whole set of n-point amplitudes is shown to be generated from one functional K(x,y;A), in addition to the induced current j(x;A).Comment: 7 pages, no figure (some comments added

New counterexamples on Ritt operators, sectorial operators and R-boundedness

Let $\mathcal D$ be a Schauder decomposition on some Banach space $X$. We prove that if $\mathcal D$ is not $R$-Schauder, then there exists a Ritt operator $T\in B(X)$ which is a multiplier with respect to $\mathcal D$, such that the set $\{T^n\, :\, n\geq 0\}$ is not $R$-bounded. Likewise we prove that there exists a bounded sectorial operator $A$ of type $0$ on $X$ which is a multiplier with respect to $\mathcal D$, such that the set $\{e^{-tA}\, : \, t\geq 0\}$ is not $R$-bounded

Functional calculus for a bounded C0C_0-semigroup on Hilbert space

We introduce a new Banach algebra ${\mathcal A}({\mathbb C}_+)$ of bounded analytic functions on ${\mathbb C}_+=\{z\in{\mathbb C}\, :\, {\rm Re}(z)>0\}$ which is an analytic version of the Figa-Talamenca-Herz algebras on ${\mathbb R}$. Then we prove that the negative generator $A$ of any bounded $C_0$-semigroup on Hilbert space $H$ admits a bounded (natural) functional calculus $\rho_A\colon {\mathcal A}({\mathbb C}_+)\to B(H)$. We prove that this is an improvement of the bounded functional calculus ${\mathcal B}({\mathbb C}_+)\to B(H)$ recently devised by Batty-Gomilko-Tomilov on a certain Besov algebra ${\mathcal B}({\mathbb C}_+)$ of analytic functions on ${\mathbb C}_+$, by showing that ${\mathcal B}({\mathbb C}_+)\subset {\mathcal A}({\mathbb C}_+)$ and ${\mathcal B}({\mathbb C}_+)\not= {\mathcal A}({\mathbb C}_+)$. In the Banach space setting, we give similar results for negative generators of $\gamma$-bounded $C_0$-semigroups. The study of ${\mathcal A}({\mathbb C}_+)$ requires to deal with Fourier multipliers on the Hardy space $H^1({\mathbb R})\subset L^1({\mathbb R})$ and we establish new results on this topic

Comparative Risk Aversion: A Formal Approach with Applications to Saving Behaviors

We consider a formal approach to comparative risk aversion and applies it to intertemporal choice models. This allows us to ask whether standard classes of utility functions, such as those inspired by Kihlstrom and Mirman [15], Selden [26], Epstein and Zin [9] and Quiggin [24] are well-ordered in terms of risk aversion. Moreover, opting for this model-free approach allows us to establish new general results on the impact of risk aversion on savings behaviors. In particular, we show that risk aversion enhances precautionary savings, clarifying the link that exists between the notions of prudence and risk aversion