A General Equilibrium Model of the Term Structure of Interest Rates under Regime-switching Risk

This paper incorporates the systematic risk of regime shifts into a general equilibrium model of the term structure of interest rates. The model shows that there is a new source of time-variation in bond term premiums in the presence of regime shifts. This new component is a regime-switching risk premium that depends on the covariations between discreet changes in marginal utility and bond prices across different regimes. A closed-form solution for the term structure of interest rates is obtained under an affine model using log-linear approximation. The model is estimated by Efficient Method of Moments. The regime-switching risk is found to be statistically significant and mostly affect the long-end of the yield curveThe Term Structure, General Equilibrium, Markov Regime Shifts

On a Kirchhoff type problems with potential well and indefinite potential

In this paper, we study the following Kirchhoff type problem:% \left\{\aligned&-\bigg(\alpha\int_{\bbr^3}|\nabla u|^2dx+1\bigg)\Delta u+(\lambda a(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\% &u\in\h,\endaligned\right.\eqno{(\mathcal{P}_{\alpha,\lambda})}% where $4<p<6$, $\alpha$ and $\lambda$ are two positive parameters, a_0\in\bbr is a (possibly negative) constant and $a(x)\geq0$ is the potential well. By the variational method, we investigate the existence of nontrivial solutions to $(\mathcal{P}_{\alpha,\lambda})$. To our best knowledge, it is the first time that the nontrivial solution of the Kirchhoff type problem is found in the indefinite case. We also obtain the concentration behaviors of the solutions as $\lambda\to+\infty$.Comment: 1

Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug

Joint Trajectory and Communication Design for UAV-Enabled Multiple Access

Unmanned aerial vehicles (UAVs) have attracted significant interest recently in wireless communication due to their high maneuverability, flexible deployment, and low cost. This paper studies a UAV-enabled wireless network where the UAV is employed as an aerial mobile base station (BS) to serve a group of users on the ground. To achieve fair performance among users, we maximize the minimum throughput over all ground users by jointly optimizing the multiuser communication scheduling and UAV trajectory over a finite horizon. The formulated problem is shown to be a mixed integer non-convex optimization problem that is difficult to solve in general. We thus propose an efficient iterative algorithm by applying the block coordinate descent and successive convex optimization techniques, which is guaranteed to converge to at least a locally optimal solution. To achieve fast convergence and stable throughput, we further propose a low-complexity initialization scheme for the UAV trajectory design based on the simple circular trajectory. Extensive simulation results are provided which show significant throughput gains of the proposed design as compared to other benchmark schemes.Comment: Submitted for possible publicatio