Regime switching dynamics in credit default swaps: Evidence from smooth transition autoregressive model

This paper investigates the dynamics of credit default swap (CDS) spread. We first find auto-correlations and cross-correlations of the CDS series and the CDS average by employing detrended cross-correlation analysis (DCCA). We then employ smooth transition autoregressive (STAR) models to characterize the regime switching behavior of 28 US corporate CDS series from January 2007 through October 2009. In each case, we find clear evidence for transitions between low-price and high-price regimes. The threshold estimations of the STAR model effectively differentiate the price regimes, where the first transition consistently coincides with the explosion of the crisis in late 2008.     

建立在同伦基础之上的一种非线性分析方法(2)——单自由度守恒系统周期的通用公式

本文以非线性的单自由度守恒系统为例,描述了一种新的非线性分析方法。此方法建立在光滑映射的基础上,不依赖于小参数,从而特别适合于求解不具有小参数的强非线性问题。本文所给近似公式的精确度对参数值的变化不敏感,对任意大小的参数都是一致有效的。     

Theory of valuations on manifolds, II

This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions.The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish some of the basic properties of it.     

Intersections of smooth polar unitals with secants are homeomorphic to spheres

In [5] and [6] we proved that (non-empty) sets of absolute points of smooth polarities, i.e. smooth polar unitals, in smooth projective planes of dimension 2l are smooth submanifolds of the point spaces homeomorphic to spheres of dimension . In this paper we show that the intersections of smooth polar unitals with secants are homeomorphic to spheres of dimension , respectively. Furthermore we prove that the condition of connectedness in [6, Theorem 1.2] may be omitted. This means that a closed (not necessarily connected) submanifold U of the point space of a smooth projective plane is homeomorphic to a sphere provided that there exists precisely one tangent at each point of U, and each secant intersects U transversally. If U has codimension 1 in the point space then the second condition follows from the first one, and also the intersections of U with secants are homeomorphic to spheres. This result may be generalized to compact hypersurfaces in the point spaces of smooth affine planes. Received: 1 July 2008     

Approximating reals by sums of rationals

We consider the question of approximating any real number α by sums of n rational numbers with denominators 1?q₁,q₂,…,qn?N. This leads to inquiries on approximating a real number by rational numbers with a prescribed number of prime factors in the denominator as well as by rational numbers with smooth denominator.     

Kolmogorov Averages and Approximate Identities

We study the action of Kolmogorov-type nonlinear averaging operators of the form V ⁻¹ AV on smooth functions. Here, A runs through a family of convolution operators A _ε ^[K], ε>0, generated by a single kernel K∈L ¹(ℝ ⁿ ) in the usual way and forming an “approximate identity” as ε→0, while V is a superposition map given by Vf=v○f, with a monotone continuous function v. The main result characterizes the kernels K with the property that the natural estimate

一类广义半无限规划问题的光滑牛顿算法

本文在广义半无限规划问题的最优解集X处满足某些条件的前提下将广义半无限规划问题转化成KKT系统,通过扰动的FB函数,将KKT系统转化为一组光滑函数方程,设计了一个光滑牛顿算法,证明了算法的全局收敛性,并且在光滑函数解集处满足局部误差界条件下证明了算法具有超线性收敛速率.