Estimation in the continuous time mover‐stayer model with an application to bond ratings migration

The usual tool for modelling bond ratings migration is a discrete, time‐homogeneous Markov chain. Such model assumes that all bonds are homogeneous with respect to their movement behaviour among rating categories and that the movement behaviour does not change over time. However, among recognized sources of heterogeneity in ratings migration is age of a bond (time elapsed since issuance). It has been observed that young bonds have a lower propensity to change ratings, and thus to default, than more seasoned bonds. The aim of this paper is to introduce a continuous, time‐non‐homogeneous model for bond ratings migration, which also incorporates a simple form of population heterogeneity. The specific form of heterogeneity postulated by the proposed model appears to be suitable for modelling the effect of age of a bond on its propensity to change ratings. This model, called a mover–stayer model, is an extension of a Markov chain. This paper derives the maximum likelihood estimators for the parameters of a continuous time mover–stayer model based on a sample of independent continuously monitored histories of the process, and develops the likelihood ratio statistic for discriminating between the Markov chain and the mover–stayer model. The methods are illustrated using a sample of rating histories of young corporate issuers. For these issuers the default probabilities predicted by the Markov chain and mover–stayer models are different. In particular for 1–4 years old bonds the mover–stayer model estimates substantially lower default probabilities from rating C than a Markov chain. Copyright © 2004 John Wiley & Sons, Ltd.     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

相对论平均场理论中各种有效相互作用对中子星性质的影响

基于相对论平均场理论，研究了各种相互作用参数组(NL1、NL3、NLSH、TM1和GL-97)对中子星物质的性质和中子星整体结构的影响．发现参数组NL1、NL3和NLSH所给出的中子星内部的介子场强度、物质的组成比例、物态方程和中子星的整体特点基本相同，但与TM1和GL-97之间有较大的差别．相对于其他参数组，GL-97给出的介子场强度最弱，中子星的相对数密度最大，物态方程也最软，同时采用GL-97参数组计算的中子星的最大质量也最小．     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

The Heat Equation with Initial Data Corrupted by Measurement Error and Missing Data

In this work the Cauchy problem for the one-dimensional heat equation is considered. In contrast to existing literature it is assumed that the initial state f is unknown and that information regarding f is obtained by some process of measurement. To enhance realism, both measurement errors and missing data are allowed for. Under assumptions on f in the Fourier-domain first an approximation to f is derived from the data by means of a novel uncertainty principle. Then, it is studied how this perturbation in the initial state propagates with time.      

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

Stability and Nonlinear Deformation of Cylindrical Grids

The general stability of single-layer cylindrical grids is studied in linear and nonlinear formulations. Dependence of the general buckling load on the geometry and stiffness parameters of a grid is established in an analytical form. Such grids are numerically analyzed for stability. It is established that the general buckling load is much less than the local buckling load. Typical general buckling modes are found. It is shown that such grids are weakly sensitive to imperfections     

期货经纪公司保证金的一种确定方法

本文基于马尔可夫链在存储论中的应用，结合Ergodic定理，得到确定期货经纪公司保证金的Ergodic模型，即一个双目标规划问题，然后应用乘积最大化准则，将该模型转化为单目标规划问题来求解。该方法考虑期货经纪公司承担的风险和对投资者的吸引程度，为保证金的确定提供新的思路。     

On the structure of the optimal server control for fluid networks

This paper derives the optimal trajectories in a general fluid network with server control. The stationary optimal policy in the complete state space is constructed. The optimal policy is constant on polyhedral convex cones. An algorithm is derived that computes these cones and the optimal policy. Generalized Klimov indices are introduced, they are used for characterizing myopic and time-uniformly optimal policies.Received: November 2004 / Revised: February 2005The research of this author has been supported by the project ‘‘Stochastic Networks’’ of the Netherlands Organisation for Scientific Research NWO.