Lorentz spaces with variable exponents

We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings and the identity . We also show that these spaces arise through real interpolation between and . Furthermore, we answer in a negative way the question posed in 12 whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.     

A new Brézis‐Gallouët‐Wainger inequality from the viewpoint of the real interpolation functors

The Brézis‐Gallouët‐Wainger inequality describes a subtle embedding property into . The relation between the Brézis‐Gallouët‐Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between and the logarithmic boundedness, which is supposed to be the right‐hand side of the Brézis‐Gallouët‐Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem.     

Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.     

一对四元数矩阵方程的共轭延拓解

定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式.     

确界原理的一个修正证明

分析了华东师大版《数学分析》（第四版）教材中关于确界原理证明的不足之处,给出更为细致的修正证明.     

A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

考虑投资者心理预期的投资性商品价格运行稳定性识别与反馈控制机制设计

以投资性商品的价格运行系统为研究对象,引入反映投资者心理预期的变量,对传统的蛛网模型加以改进,并据此构建非均衡市场环境下投资性商品价格运行开环系统模型,对非均衡市场环境下投资性商品市场价格运行的稳定性进行识别,在此基础上对反馈控制机制进行设计.以我国的住宅市场的价格运行系统为实证研究对象,结合历史数据对所构模型的有效性进行验证,并对未来可能出现情况进行预测.实证研究主要结论如下:第一,我国住宅市场投资者对预期收益的敏感程度以及供应商对商品前期价格的敏感程度均较高,价格运行能自发实现稳定的区域较小;第二,现有调控政策不变的情况下,我国住宅市场价格正向偏离稳定区域的程度将减小;第三,若政府从影响投资者心理预期的角度入手对我国住宅市场价格波动进行干预,希望我国住宅市场的价格运行能以最快的速度趋于稳态,则设计反馈控制机制时,应重视投资者对商品价格未来的心理预期受商品历史价格的影响程度远高于受市场供需的影响程度这一现象.     

R&D投入、技术溢出及吸收能力与经济增长的空间计量分析

利用我国31个省份2001-2010年的面板数据,使用空间滞后模型(SLM)研究了我国区域RD投入、空间溢出效应及吸收能力对经济增长的影响.研究结果表明我国各省份经济增长之间存在着高度的空间相关性,一个省份的RD投入不仅能够促进本地区的经济增长,还会通过技术溢出促进相邻地区的经济增长,同时一个地区吸收能力越强,其对该地区经济增长的影响也越大.     

基于状态空间模型构建我国固定资产投资的SWI景气指数

从众多经济指标中选取了固定资产投资的先行、一致指标组,利用所选择的指标基于状态空间模型,采用Kalman滤波估计方法得到了固定资产投资的一致和先行SWI景气指数.对一致指数的分析表明,自1998年以来我国固定资产投资经历了蓬勃扩张的投资长周期和两轮振荡波动的投资短周期,从2008年开始在国际金融危机蔓延和我国经济结构调整的大背景下固定资产投资进入相对平稳增长期.通过对先行合成指数的分析,认为"十二五"期间投资将保持稳定增长,出现大起大落的可能性很小.