One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

综合评价中一种凹性指数型功效函数

目前主流功效函数多为凸性,在处理社会经济数据集中常见的右偏样本时效果难以令人满意。通过系统探讨凸性和凹性功效函数各自的适用特征,指出凹性函数在应用中有其必要性。归纳并使用偏度、区分度、P-P图三种方法作为分布形态的评判标准,比较了常见功效函数对指标原始数据分布形态的调整作用。在分析基础上,提出一种改进的凹性指数功效函数,能有效地处理右偏数据,且相比使用对数预处理的凸性功效函数更具适用性与便利性。     

基于凸度缺口模型的商业银行利率风险最优控制及其应用

对商业银行利率风险的管理和控制,传统的久期模型仅适用于利率变化较小和利率期限结构平移条件下的线性近似估计,否则就需要运用凸度进行调整。根据Markowitz现代组合投资理论,构造一个目标规划模型,通过合理确定其中决策变量的值,使商业银行在决策期末满足最小化利率风险和银行资产负债组合的凸度为非负的条件下收益最大化。计算实例表明,凸度缺口模型对于给定的初始值和约束条件,可以较好地减少利率风险的暴露头寸和提高收益;同时,利率风险较大时凸度缺口模型比久期缺口模型更好地减少风险暴露,鲁棒性(robustness)更强。     

矩阵秩的下界估计与Schur不等式的改进

研究具有实用价值的关于一般复方阵的非奇准则、秩的下界实用估计,特征值实部和虚部的平方和上界估计,所得结果改进了著名的 Schur 不等式和 Ky Fan-Hoffman 不等式的估计。     

实共轭空间X~*严格凸的一个充分条件

证明了定理 :设X是实Banach空间 ,S是X的单位球面 ,如果存在p >0 ,q >0 ,p +q =1,使得lim　r→ 0 +sup0 <‖u -v‖ 相似文献   

Stochastic comparisons of order statistics,with applications in relibility

This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G^?1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described     

Why a time effect often has a limited impact on capture‐recapture estimates in closed populations

The author is concerned with log‐linear estimators of the size N of a population in a capture‐recapture experiment featuring heterogeneity in the individual capture probabilities and a time effect. He also considers models where the first capture influences the probability of subsequent captures. He derives several results from a new inequality associated with a dispersive ordering for discrete random variables. He shows that in a log‐linear model with inter‐individual heterogeneity, the estimator N is an increasing function of the heterogeneity parameter. He also shows that the inclusion of a time effect in the capture probabilities decreases N in models without heterogeneity. He further argues that a model featuring heterogeneity can accommodate a time effect through a small change in the heterogeneity parameter. He demonstrates these results using an inequality for the estimators of the heterogeneity parameters and illustrates them in a Monte Carlo experiment     

债券的利率风险测度及套期保值策略

利率水平的涨落 ,会使债券持有者资本利得相应的增加或损失 ,这种风险称为债券的利率风险。首先解释了债券的定价及利率风险的原理 ,继而给出了利率风险较为流行的测度方法 ,即久期 (Durability)、修正久期(ModifiedDurabilityorSensitivity) ,并用图示的方法指出了久期测度风险的不足 ,然后将债券价格波动作泰勒展开 ,取其前两项 ,把凸度的因素考虑在内 ,从而这种波动精确到二阶无穷小 ,基本满足了实际中的运用。在久期和凸度的基础上 ,当收益率曲线水平移动时 ,给出了对暴露在利率风险下的固定收益债券的套期保值的具体策略。     

A General Model of Random Variation

A statistical distribution of a random variable is uniquely represented by its normal-based quantile function. For a symmetrical distribution it is S-shaped (for negative kurtosis) and inverted S-shaped (otherwise). As skewness departs from zero, the quantile function gradually transforms into a monotone convex function (positive skewness) or concave function (otherwise). Recently, a new general modeling platform has been introduced, response modeling methodology, which delivers good representation to monotone convex relationships due to its unique “continuous monotone convexity” property. In this article, this property is exploited to model the normal-based quantile function, and explored using a set of 27 distributions.