风险函数

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

This dissertation is devoted to studying the ruin theory on the dual risk model with several dividend rates and on the bidimensional perturbed risk model with or without stochastic disturbance, which includes the discounted expected function about the dual risk model with three dividend rates and the ruin probability on the bidimensional perturbed risk model.

本文致力于研究分多段分红的对偶风险模型及二维风险模型的破产理论，主要研究了分三段分红的对偶风险模型的折现红利的期望函数，并对带有扰动项的二维风险模型的破产概率做了研究。

Under the concave transaction costs function, using the variance of profolio return rate to express profolio risk, and taking the risk-return combination difference as the objective function, we propose Mean-variance D.C- integer optimization model under concave transaction costs and minimal transaction unit constraints.

2考虑凹交易费用函数，用投资组合收益率的方差反映组合风险，以风险-收益的组合差作为目标函数，提出了考虑交易费用及最小交易量的均值—方差D.C-整数优化模型。

Firstly, variables which were acquired for the above two kinds of classification system were obtained from field and laboratory investigation of the core samples as well as test of supersonic waves in drilling holes. Secondly, distribution functions and parameters of all variables are determined using statistic method. Thirdly, 20000 RMR values or BQ values and cumulative distribution function of these RMR or BQ values have been obtained utilizing Monte—Carlo method and the results are plotted. Finally, risk analysis can be made from above results.

风险评价方法步骤如下：（1）首先通过岩芯样品的现场观测和实验室试验及钻孔岩体超声波测试获得两种分类所需的变量；（2）通过统计分析和判断得出各变量的分布函数及参数；（3）运用Monte—Carlo模拟方法获得2万个RMR值或BQ值及相应的累积分布函数，并将结果绘成岩体质量描述图；（4）运用以上结果作出岩体质量风险分析。

In order to expose more exactly of the market risk faced by financing institutions, and manage risk more deeply and completely, This article expands research in the following aspects: multivariate abnormal distribution family, the measurement of correlation function in the portfolio selection and Copula function.

为了能更准确地反映金融机构面临的市场风险，进行深层次的、全面的管理金融风险，本文最后从以下几方面展开了风险价值度量方法的研究：多元非正态分布族，投资组合中相关性度量方法及Copula函数。

In order to expose more exactly of the market risk faced by financing institutions,and manage risk more deeply and completely,This article expands research in the following aspects:multivariate abnormal distribution family,the measurement of correlati on function in the portfolio selection and Copula function.

为了能更准确地反映金融机构面临的市场风险，入行深层次的、全面的管理金融风险，本文最后从以下几方面展开了风险价值度量方法的研究：多元非正态分布族，投资组合中相关性度量方法及Copula函数。

Therefore an artificial nervenetwork with better effect of imminence should be designed so that it can be used in the field of technological innovation and achieve good results.

本文利用径向基函数神经网络这一技术手段，提出了基于径向基函数神经网络的技术创新风险评价模型，为技术创新项目的风险评价提出了一种新颖、高效的方法。

By the minimum risk Bayes decision theory, this paper develops a new way of image segmentation: establish the mathematics model of image segmentation; estimate the probability density of grey scales and figure out its math-expectation and square difference that accord with normal distribution and the loss function; and judge the every pixel dot in the image according to the minimum risk Bayes decision theory and determine whether it is of target or non-target images, thereby realizing the extraction of the target image.

依据最小风险贝叶斯决策理论，提出了一种基于最小风险贝叶斯决策的图像分割方法。首先建立图像分割的最小风险贝叶斯决策模型，对灰度级类条件概率密度估计出其符合正态分布的数学期望和方差以及损失函数，再依据最小风险贝叶斯决策理论对图像中的每一像素点进行目标图像和非目标图像的类别判断，从而实现目标图像的提取。

Firstly, the basic concepts of risk are introduced, and the relation between risk and probability distribution, and the utility function are analysed.

本文首先介绍了风险基本概念、风险与概率分布的关系、风险与效用函数等，总结了国内外风险管理发展概况。

In this paper, we contribute an evolutionary heterogeneous beliefs model byusing t distribution to replace traditional standard normal to describe fundamen-tal price process and adding risk-adjusted market fraction function in classicaltwo types traders scheme. And then we utilizedifference equation stability and bifurcation theory and numerical simulation tostudy the system. It is found that the system has some styled facts (high kurto-sis、fat tali and long memory) of the actual financial market, and this indicatesthat the simulation model can reflect well the true financial market.

本文通过引入t分布代替原有的正态分布描述基础价格过程，引入经风险调整的投资者市场分数维函数取代原有的无风险调整的市场分数维函数，在经典的两类投资者(自主投资者和图表分析者)模拟模型框架下，建立了新的异质预期资产定价模型，利用差分方程稳定性和分支理论及数值模拟的方法对该系统进行理论分析和实证研究，发现模型具有真实金融市场的程式化事实(尖峰厚尾性，长记忆性等)，模拟效果较好。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。